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Journal articles on the topic 'ENO (Essentially Non-Oscillatory) and WENO method.]'

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Published: 11 March 2023

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1

Janett, Gioele, Oskar Steiner, Ernest Alsina Ballester, Luca Belluzzi, and Siddhartha Mishra. "A novel fourth-order WENO interpolation technique." Astronomy & Astrophysics 624 (April 2019): A104. http://dx.doi.org/10.1051/0004-6361/201834761.

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Context. Several numerical problems require the interpolation of discrete data that present at the same time (i) complex smooth structures and (ii) various types of discontinuities. The radiative transfer in solar and stellar atmospheres is a typical example of such a problem. This calls for high-order well-behaved techniques that are able to interpolate both smooth and discontinuous data. Aims. This article expands on different nonlinear interpolation techniques capable of guaranteeing high-order accuracy and handling discontinuities in an accurate and non-oscillatory fashion. The final aim i

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2

Shu, Chi-Wang. "Essentially non-oscillatory and weighted essentially non-oscillatory schemes." Acta Numerica 29 (May 2020): 701–62. http://dx.doi.org/10.1017/s0962492920000057.

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Essentially non-oscillatory (ENO) and weighted ENO (WENO) schemes were designed for solving hyperbolic and convection–diffusion equations with possibly discontinuous solutions or solutions with sharp gradient regions. The main idea of ENO and WENO schemes is actually an approximation procedure, aimed at achieving arbitrarily high-order accuracy in smooth regions and resolving shocks or other discontinuities sharply and in an essentially non-oscillatory fashion. Both finite volume and finite difference schemes have been designed using the ENO or WENO procedure, and these schemes are very popula

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Schmidt, Alex A., Alice de Jesus Kozakevicius, and Stefan Jakobsson. "A parallel wavelet adaptive WENO scheme for 2D conservation laws." International Journal of Numerical Methods for Heat & Fluid Flow 27, no. 7 (2017): 1467–86. http://dx.doi.org/10.1108/hff-08-2016-0295.

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Purpose The current work aims to present a parallel code using the open multi-processing (OpenMP) programming model for an adaptive multi-resolution high-order finite difference scheme for solving 2D conservation laws, comparing efficiencies obtained with a previous message passing interface formulation for the same serial scheme and considering the same type of 2D formulations laws. Design/methodology/approach The serial version of the code is naturally suitable for parallelization because the spatial operator formulation is based on a splitting scheme per direction for which the flux compone

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Kuo, F. A., and J. S. Wu. "Implementation of a parallel high-order WENO-type Euler equation solver using a CUDA PTX paradigm." Journal of Mechanics 37 (2021): 496–512. http://dx.doi.org/10.1093/jom/ufab016.

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ABSTRACT This study proposes the optimization of a low-level assembly code to reconstruct the flux for a splitting flux Harten–Lax–van Leer (SHLL) scheme on high-end graphic processing units. The proposed solver is implemented using the weighted essentially non-oscillatory reconstruction method to simulate compressible gas flows that are derived using an unsteady Euler equation. Instructions in the low-level assembly code, i.e. parallel thread execution and instruction set architecture in compute unified device architecture (CUDA), are used to optimize the CUDA kernel for the flux reconstructi

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Wolf, W. R., and J. L. F. Azevedo. "IMPLEMENTATION OF ENO AND WENO SCHEMES FOR FINITE VOLUME UNSTRUCTURED GRID SOLUTIONS OF COMPRESSIBLE AERODYNAMIC FLOWS." Revista de Engenharia Térmica 6, no. 1 (2007): 48. http://dx.doi.org/10.5380/reterm.v6i1.61817.

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In this work the essentially non-oscillatory schemes (ENO) and the weighted essentially non-oscillatory schemes (WENO) are implemented in a cell centered finite volume context on unstructured meshes. The 2-D Euler equations will be considered to represent the flows of interest. The ENO and WENO schemes have been developed with the purpose of accurately capturing discontinuities appearing in problems governed by hyperbolic conservation laws. In the high Mach number aerodynamic studies of interest in the present paper, these discontinuities are mainly represented by shock waves and contact disco

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Kadioglu, Samet Y., and Veli Colak. "An Essentially Non-Oscillatory Spectral Deferred Correction Method for Conservation Laws." International Journal of Computational Methods 13, no. 05 (2016): 1650027. http://dx.doi.org/10.1142/s0219876216500274.

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We present a computational method based on the Spectral Deferred Corrections (SDC) time integration technique and the Essentially Non-Oscillatory (ENO) finite volume method for the conservation laws (one-dimensional Euler equations). The SDC technique is used to advance the solutions in time with high-order of accuracy. The ENO method is used to define high-order cell edge quantities that are then used to evaluate numerical fluxes. The coupling of the SDC method with a high-order finite volume method (Piece-wise Parabolic Method (PPM)) for solving the conservation laws is first carried out by

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Zhu, Jun, and Jianxian Qiu. "Runge-Kutta Discontinuous Galerkin Method Using Weno-Type Limiters: Three-Dimensional Unstructured Meshes." Communications in Computational Physics 11, no. 3 (2012): 985–1005. http://dx.doi.org/10.4208/cicp.300810.240511a.

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AbstractThis paper further considers weighted essentially non-oscillatory (WENO) and Hermite weighted essentially non-oscillatory (HWENO) finite volume methods as limiters for Runge-Kutta discontinuous Galerkin (RKDG) methods to solve problems involving nonlinear hyperbolic conservation laws. The application discussed here is the solution of 3-D problems on unstructured meshes. Our numerical tests again demonstrate this is a robust and high order limiting procedure, which simultaneously achieves high order accuracy and sharp non-oscillatory shock transitions.

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Wang, Zhenming, Jun Zhu, Chunwu Wang, and Ning Zhao. "Finite difference alternative unequal-sized weighted essentially non-oscillatory schemes for hyperbolic conservation laws." Physics of Fluids 34, no. 11 (2022): 116108. http://dx.doi.org/10.1063/5.0123597.

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In this paper, two unequal-sized weighted essentially non-oscillatory (US-WENO) schemes are proposed for solving hyperbolic conservation laws. First, an alternative US-WENO (AUS-WENO) scheme based directly on the values of conserved variables at the grid points is designed. This scheme can inherit all the advantages of the original US-WENO scheme [J. Zhu and J. Qiu, “A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws,” J. Comput. Phys. 318, 110–121 (2016).], such as the arbitrariness of the linear weights. Moreover, this presented AUS-WENO scheme enables a

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9

Zhu, Jun, Xinghui Zhong, Chi-Wang Shu, and Jianxian Qiu. "Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter." Communications in Computational Physics 19, no. 4 (2016): 944–69. http://dx.doi.org/10.4208/cicp.070215.200715a.

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AbstractIn this paper, we propose a new type of weighted essentially non-oscillatory (WENO) limiter, which belongs to the class of Hermite WENO (HWENO) limiters, for the Runge-Kutta discontinuous Galerkin (RKDG) methods solving hyperbolic conservation laws. This new HWENO limiter is a modification of the simple WENO limiter proposed recently by Zhong and Shu [29]. Both limiters use information of the DG solutions only from the target cell and its immediate neighboring cells, thus maintaining the original compactness of the DG scheme. The goal of both limiters is to obtain high order accuracy a

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10

Antona, Rubén, Renato Vacondio, Diego Avesani, Maurizio Righetti, and Massimiliano Renzi. "Towards a High Order Convergent ALE-SPH Scheme with Efficient WENO Spatial Reconstruction." Water 13, no. 17 (2021): 2432. http://dx.doi.org/10.3390/w13172432.

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This paper studies the convergence properties of an arbitrary Lagrangian–Eulerian (ALE) Riemann-based SPH algorithm in conjunction with a Weighted Essentially Non-Oscillatory (WENO) high-order spatial reconstruction, in the framework of the DualSPHysics open-source code. A convergence analysis is carried out for Lagrangian and Eulerian simulations and the numerical results demonstrate that, in absence of particle disorder, the overall convergence of the scheme is close to the one guaranteed by the WENO spatial reconstruction. Moreover, an alternative method for the WENO spatial reconstruction

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ZHU, JUN, NING ZHAO, and HUASHENG ZHENG. "HIGH ORDER LOCALIZED ENO SCHEMES ON UNSTRUCTURED MESHES FOR CONSERVATION LAWS." Modern Physics Letters B 19, no. 28n29 (2005): 1563–66. http://dx.doi.org/10.1142/s0217984905009912.

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We construct a localized finite volume method by applying ENO (essentially non-oscillatory) reconstruction to solve hyperbolic conservation laws following the partitions of the spectral volume methods. The main idea is as follows: Firstly, separate the calculating domain into intervals, named main-cells, then divide the intervals into subintervals, named sub-cells. Secondly, use ENO methodology to reconstruct conservative variables in the main-cells by using the cell averages of proper sub-cells. After that, use the TVD Runge-Kutta time discrete method to obtain fully discrete scheme. Several

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DENG, FENG, and YI-ZHAO WU. "A HYBRID RECONSTRUCTION STRATEGY FOR FULLY ADAPTIVE MULTI-RESOLUTION SCHEME." Modern Physics Letters B 23, no. 03 (2009): 333–36. http://dx.doi.org/10.1142/s0217984909018333.

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In this paper we propose a second order hybrid reconstruction strategy for the fully adaptive multi-resolution scheme based on the second order finite volume method. The fully adaptive multi-resolution scheme is an adaptive grid method for solving the hyperbolic conservation laws. To improve its robustness, the third order central reconstruction is replaced by the second order hybrid reconstruction, i.e. the anti-ENO (essentially non-oscillatory) reconstruction and the ENO reconstruction have been adopted for the multi-resolution analysis and the inverse multi-resolution analysis, respectively

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Frenzel, David, and Jens Lang. "A third-order weighted essentially non-oscillatory scheme in optimal control problems governed by nonlinear hyperbolic conservation laws." Computational Optimization and Applications 80, no. 1 (2021): 301–20. http://dx.doi.org/10.1007/s10589-021-00295-2.

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AbstractThe weighted essentially non-oscillatory (WENO) methods are popular and effective spatial discretization methods for nonlinear hyperbolic partial differential equations. Although these methods are formally first-order accurate when a shock is present, they still have uniform high-order accuracy right up to the shock location. In this paper, we propose a novel third-order numerical method for solving optimal control problems subject to scalar nonlinear hyperbolic conservation laws. It is based on the first-disretize-then-optimize approach and combines a discrete adjoint WENO scheme of t

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14

Chen, Shanqin. "Krylov SSP Integrating Factor Runge–Kutta WENO Methods." Mathematics 9, no. 13 (2021): 1483. http://dx.doi.org/10.3390/math9131483.

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Weighted essentially non-oscillatory (WENO) methods are especially efficient for numerically solving nonlinear hyperbolic equations. In order to achieve strong stability and large time-steps, strong stability preserving (SSP) integrating factor (IF) methods were designed in the literature, but the methods there were only for one-dimensional (1D) problems that have a stiff linear component and a non-stiff nonlinear component. In this paper, we extend WENO methods with large time-stepping SSP integrating factor Runge–Kutta time discretization to solve general nonlinear two-dimensional (2D) probl

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15

Vega, Carlos A., and Francisco Arias. "Numerical Simulations of a Polydisperse Sedimentation Model by Using Spectral WENO Method with Adaptive Multiresolution." International Journal of Computational Methods 13, no. 06 (2016): 1650037. http://dx.doi.org/10.1142/s0219876216500377.

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In this work, we apply adaptive multiresolution (Harten’s approach) characteristic-wise fifth-order Weighted Essentially Non-Oscillatory (WENO) for computing the numerical solution of a polydisperse sedimentation model, namely, the Höfler and Schwarzer model. In comparison to other related works, time discretization is carried out with the ten-stage fourth-order strong stability preserving Runge–Kutta method which is more efficient than the widely used optimal third-order TVD Runge–Kutta method. Numerical results with errors, convergence rates and CPU times are included for four and 11 species

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Nguyen, Binh Huy, and Giang Song Le. "Comparative study of numerical schemes for strong shock simulation using the Euler equations." Science and Technology Development Journal 18, no. 1 (2015): 73–88. http://dx.doi.org/10.32508/stdj.v18i1.943.

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A numerical study of extremely strong shocks was presented. Various types of numerical schemes with first-order accuracy and higherorder accuracy with adaptive stencils were implemented to solve the one and twodimensional Euler equations based on the explicit finite difference method, including Roe’s first-order upwind, Steger-Warming Flux Vector splitting (FVS), Sweby’s flux-limited and Essentially Non-oscillatory (ENO) scheme. The result comparisons were carried out to discuss which scheme is the most suitable for strong shock problem. The dissipative nature of the firstorder scheme can be e

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Kozakevicius, Alice de Jesus, Dia Zeidan, Alex A. Schmidt, and Stefan Jakobsson. "Solving a mixture model of two-phase flow with velocity non-equilibrium using WENO wavelet methods." International Journal of Numerical Methods for Heat & Fluid Flow 28, no. 9 (2018): 2052–71. http://dx.doi.org/10.1108/hff-05-2017-0215.

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Purpose The purpose of this work is to present the implementation of weighted essentially non-oscillatory (WENO) wavelet methods for solving multiphase flow problems. The particular interest is gas–liquid two-phase mixture with velocity non-equilibrium. Numerical simulations are carried out on different scenarios of one-dimensional Riemann problems for gas–liquid flows. Results are validated and qualitatively compared with solutions provided by other standard numerical methods. Design/methodology/approach This paper extends the framework of WENO wavelet adaptive method to a fully hyperbolic tw

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18

Yang, Jie, and Song Ping Wu. "An Immersed Boundary Method for Compressible Flows with Complex Boundaries." Applied Mechanics and Materials 477-478 (December 2013): 281–84. http://dx.doi.org/10.4028/www.scientific.net/amm.477-478.281.

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An immersed boundary method based on the ghost-cell approach is presented in this paper. The compressible Navier-Stokes equations are discretized using a flux-splitting method for inviscid fluxes and second-order central-difference for the viscous components. High-order accuracy is achieved by using weighted essentially non-oscillatory (WENO) and Runge-Kutta schemes. Boundary conditions are reconstructed by a serial of linear interpolation and inverse distance weighting interpolation of flow variables in fluid domain. Two classic flow problems (flow over a circular cylinder, and a NACA 0012 ai

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Sun, Ziyao, Honghui Teng, and Feng Xiao. "A Slope Constrained 4th Order Multi-Moment Finite Volume Method with WENO Limiter." Communications in Computational Physics 18, no. 4 (2015): 901–30. http://dx.doi.org/10.4208/cicp.081214.250515s.

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AbstractThis paper presents a new and better suited formulation to implement the limiting projection to high-order schemes that make use of high-order local reconstructions for hyperbolic conservation laws. The scheme, so-called MCV-WENO4 (multi-moment Constrained finite Volume with WENO limiter of 4th order) method, is an extension of the MCV method of Ii & Xiao (2009) by adding the 1st order derivative (gradient or slope) at the cell center as an additional constraint for the cell-wise local reconstruction. The gradient is computed from a limiting projection using the WENO (weighted esse

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Kim, Seongjai, and Richard Cook. "3-D traveltime computation using second‐order ENO scheme." GEOPHYSICS 64, no. 6 (1999): 1867–76. http://dx.doi.org/10.1190/1.1444693.

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We consider a second‐order finite difference scheme to solve the eikonal equation. Upwind differences are requisite to sharply resolve discontinuities in the traveltime derivatives, whereas centered differences improve the accuracy of the computed traveltime. A second‐order upwind essentially non‐oscillatory (ENO) scheme satisfies these requirements. It is implemented with a dynamic down ’n’ out (DNO) marching, an expanding box approach. To overcome the instability of such an expanding box scheme, the algorithm incorporates an efficient post sweeping (PS), a correction‐by‐iteration method. Nea

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Sun, Yan, Yongjie Shi, and Guohua Xu. "Application of High-Order WENO Scheme in the CFD/FW–H Method to Predict Helicopter Rotor Blade–Vortex Interaction Tonal Noise." Aerospace 9, no. 4 (2022): 196. http://dx.doi.org/10.3390/aerospace9040196.

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The accurate prediction of helicopter rotor blade–vortex interaction (BVI) noise is challenging. This paper presents an implementation of the seventh-order improved weighted essentially non-oscillatory (WENO-Z) scheme for predicting rotor BVI noise using a high-resolution numerical method based on the Reynolds-averaged Navier–Stokes and the Ffowcs Williams–Hawkings equations. The seventh-order improved WENO-Z scheme is utilized to minimize the inherent numerical dissipation of the reconstruction method in the monotone upstream-centered scheme for conservation laws (MUSCL), thereby improving th

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Jiang, Zhenhua, Chao Yan, Jian Yu, and Boxi Lin. "Designing Several Types of Oscillation-Less and High-Resolution Hybrid Schemes on Block-Structured Grids." Communications in Computational Physics 21, no. 5 (2017): 1376–407. http://dx.doi.org/10.4208/cicp.oa-2015-0028.

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AbstractAn idea of designing oscillation-less and high-resolution hybrid schemes is proposed and several types of hybrid schemes based on this idea are presented on block-structured grids. The general framework, for designing various types of hybrid schemes, is established using a Multi-dimensional Optimal Order Detection (MOOD) method proposed by Clain, Diot and Loubère [1]. The methodology utilizes low dissipation or dispersion but less robust schemes to update the solution and then implements robust and high resolution schemes to deal with problematic situations. A wide range of computation

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Don, Wai-Sun, Antonio de Gregorio, Jean-Piero Suarez, and Gustaaf B. Jacobs. "Assessing the Performance of a Three Dimensional Hybrid Central-WENO Finite Difference scheme with Computation of a Sonic Injector in Supersonic Cross Flow." Advances in Applied Mathematics and Mechanics 4, no. 06 (2012): 719–36. http://dx.doi.org/10.4208/aamm.12-12s03.

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AbstractA hybridization of a high order WENO-Zfinite difference scheme and a high order central finite difference method for computation of the two-dimensional Euler equations first presented in [B. Costa and W. S. Don, J. Comput. Appl. Math., 204(2) (2007)] is extended to three-dimensions and for parallel computation. The Hybrid scheme switches dynamically from a WENO-Zscheme to a central scheme at any grid location and time instance if the flow is sufficiently smooth and vice versa if the flow is exhibiting sharp shock-type phenomena. The smoothness of the flow is determined by a high order

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Abedian, Rooholah. "High-Order Semi-Discrete Central-Upwind Schemes with Lax–Wendroff-Type Time Discretizations for Hamilton–Jacobi Equations." Computational Methods in Applied Mathematics 18, no. 4 (2018): 559–80. http://dx.doi.org/10.1515/cmam-2017-0031.

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AbstractA new fifth-order, semi-discrete central-upwind scheme with a Lax–Wendroff time discretization procedure for solving Hamilton–Jacobi (HJ) equations is presented. This is an alternative method for time discretization to the popular total variation diminishing (TVD) Runge–Kutta time discretizations. Unlike most of the commonly used high-order upwind schemes, the new scheme is formulated as a Godunov-type method. The new scheme is based on the flux Kurganov, Noelle and Petrova (KNP flux). The spatial discretization is based on a symmetrical weighted essentially non-oscillatory reconstruct

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Kasem, Tamer, and Jun Sasaki. "MULTIPHASE MODELING OF WAVE PROPAGATION OVER SEMICIRCULAR OBSTACLES USING WENO AND LEVEL SET METHODS." Coastal Engineering Proceedings 1, no. 32 (2011): 57. http://dx.doi.org/10.9753/icce.v32.waves.57.

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Wave propagation over a semicircular obstacle is studied. This problem is related to the design of semicircular breakwaters. These breakwaters are expected to have enhanced stability and were constructed in various places in China. Enhanced numerical modeling is done taking viscosity into account. The fifth order space accurate weighted essentially non-oscillatory (WENO) method is used to discretize the convection terms. As a result accurate results are obtained using simple options (uniform Cartesian grid, level set method). Wave generation is done using a numerical piston wave maker that is

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Liu, Zhi Lin, and Yong Huang. "Comparison of the Interface-Capturing Behavior between LSM and MCLS." Key Engineering Materials 730 (February 2017): 533–40. http://dx.doi.org/10.4028/www.scientific.net/kem.730.533.

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Numerical simulation of the moving interface is widely investigated in the fields of two-phase flow, crystal growth, molten metal casting and so on. To simulate accurately and quickly motion state of the moving interface, two types of interface-capturing method, LSM (level set method) and MCLS (mass-conserving LSM coupled with VOF (volume of fluid)), were comparatively analysed and studied. Two kinds of moving interface, rotation motion of Zaleska slotted disk interface and shearing deformation of the circle interface, were simulated. The level set advection equation was solved with IATVD (the

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Scandaliato, Angelo L., and Meng-Sing Liou. "AUSM-Based High-Order Solution for Euler Equations." Communications in Computational Physics 12, no. 4 (2012): 1096–120. http://dx.doi.org/10.4208/cicp.250311.081211a.

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AbstractIn this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method (AUSM), specifically AUSM+-UP, with high-order upwind-biased interpolation procedures, the weighted essentially non-oscillatory (WENO-JS) scheme and its variations, and the monotonicity preserving (MP) scheme, for solving the Euler equations. MP is found to be more effective than the three WENO variations studied. AUSM+-UP is also shown to be free of the so-called “carbuncle” phenomenon with the high-order interpolation. The characteristic variables are preferred for interpolatio

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Wang, Cheng, and Xinqiao Liu. "High Resolution Numerical Simulation of Detonation Diffraction of Condensed Explosives." International Journal of Computational Methods 12, no. 02 (2015): 1550005. http://dx.doi.org/10.1142/s021987621550005x.

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In this paper, the specific expression for pressure and sound speed in chemical reaction zone of condensed explosives are theoretically deduced, and a new method for deriving the partial derivative of pressure in respect of every conserved quantity is proposed. Combined with the third-order TVD Runge–Kutta method, we develop a parallel solver using the fifth-order high-resolution weighted essentially non-oscillatory (WENO) finite difference scheme to simulate detonation diffraction for two-dimensional condensed explosives. The numerical simulation results revealed the forming reasons of the lo

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Zhu, Jun, Xinghui Zhong, Chi-Wang Shu, and Jianxian Qiu. "Runge-Kutta Discontinuous Galerkin Method with a Simple and Compact Hermite WENO Limiter on Unstructured Meshes." Communications in Computational Physics 21, no. 3 (2017): 623–49. http://dx.doi.org/10.4208/cicp.221015.160816a.

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AbstractIn this paper we generalize a new type of compact Hermite weighted essentially non-oscillatory (HWENO) limiter for the Runge-Kutta discontinuous Galerkin (RKDG) method, which was recently developed in [38] for structured meshes, to two dimensional unstructured meshes. The main idea of this HWENO limiter is to reconstruct the new polynomial by the usage of the entire polynomials of the DG solution from the target cell and its neighboring cells in a least squares fashion [11] while maintaining the conservative property, then use the classical WENO methodology to form a convex combination

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Zahran, Y. H. "Fully and Semi-discrete Fourth-order Schemes for Hyperbolic Conservation Laws." Computational Methods in Applied Mathematics 7, no. 3 (2007): 264–82. http://dx.doi.org/10.2478/cmam-2007-0017.

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AbstractA new fourth order accurate centered finite difference scheme for the solution of hyperbolic conservation laws is presented. A technique of making the fourth order scheme TVD is presented. The resulting scheme can avoid spurious oscillations and preserve fourth order accuracy in smooth parts. We discuss the extension of the TVD scheme to the nonlinear scalar hyperbolic conservation laws. For nonlinear systems, the TVD constraint is applied by solving shallow water equations. Then, we propose to use this fourth order flux as a building block in spatially fifth order weighted essentially

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Pei, Weicheng, Yuyan Jiang, and Shu Li. "High-Order CFD Solvers on Three-Dimensional Unstructured Meshes: Parallel Implementation of RKDG Method with WENO Limiter and Momentum Sources." Aerospace 9, no. 7 (2022): 372. http://dx.doi.org/10.3390/aerospace9070372.

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In aerospace engineering, high-order computational fluid dynamics (CFD) solvers suitable for three-dimensional unstructured meshes are less developed than expected. The Runge–Kutta discontinuous Galerkin (RKDG) finite element method with compact weighted essentially non-oscillatory (WENO) limiters is one of the candidates, which might give high-order solutions on unstructured meshes. In this article, we provide an efficient parallel implementation of this method for simulating inviscid compressible flows. The implemented solvers are tested on lower-dimensional model problems and real three-dim

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Sharma, Dipty, Paramjeet Singh, Ravi P. Agarwal, and Mehmet Emir Koksal. "Numerical Approximation for Nonlinear Noisy Leaky Integrate-and-Fire Neuronal Model." Mathematics 7, no. 4 (2019): 363. http://dx.doi.org/10.3390/math7040363.

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We consider a noisy leaky integrate-and-fire (NLIF) neuron model. The resulting nonlinear time-dependent partial differential equation (PDE) is a Fokker-Planck Equation (FPE) which describes the evolution of the probability density. The finite element method (FEM) has been proposed to solve the governing PDE. In the realistic neural network, the irregular space is always determined. Thus, FEM can be used to tackle those situations whereas other numerical schemes are restricted to the problems with only a finite regular space. The stability of the proposed scheme is also discussed. A comparison

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Kajikawa, Yuki, Masamitsu Kuroiwa, and Naohiro Otani. "NUMERICAL SIMULATION OF THREE-DIMENSIONAL FLOW AROUND HARBOR DUE TO TSUNAMI USING FAVOR METHOD AND WENO SCHEME." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 71. http://dx.doi.org/10.9753/icce.v36.papers.71.

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In this paper, a three-dimensional (3D) tsunami flow model was proposed in order to predict a 3D flow field around a harbor accurately when tsunami strikes. In the proposed numerical model, the Cartesian coordinate system was adopted, and the Fractional Area/Volume Obstacle Representation (FAVOR) method, which has the ability to impose boundary conditions smoothly at complex boundaries, was introduced into the governing equations in consideration of applying the estimation to actual harbors with complex shape in the future. Moreover, the fifth-order Weighted Essentially Non- Oscillatory (WENO)

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Um, Kiwon, Xiangyu Hu, Bing Wang, and Nils Thuerey. "Spot the Difference." ACM Transactions on Applied Perception 18, no. 2 (2021): 1–15. http://dx.doi.org/10.1145/3449064.

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Comparative evaluation lies at the heart of science, and determining the accuracy of a computational method is crucial for evaluating its potential as well as for guiding future efforts. However, metrics that are typically used have inherent shortcomings when faced with the under-resolved solutions of real-world simulation problems. We show how to leverage the human visual system in conjunction with crowd-sourced user studies to address the fundamental problems of widely used classical evaluation metrics. We demonstrate that such user studies driven by visual perception yield a very robust met

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WANG, Zhexu, Rei KAWASHIMA, and Kimiya KOMURASAKI. "A fast convergence fourth-order Vlasov model for Hall thruster ionization oscillation analyses." Plasma Science and Technology 24, no. 2 (2021): 025502. http://dx.doi.org/10.1088/2058-6272/ac3970.

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Abstract A 1D1V hybrid Vlasov-fluid model was developed for this study to elucidate discharge current oscillations of Hall thrusters (HTs). The Vlasov equation for ions velocity distribution function with ionization source term is solved using a constrained interpolation profile conservative semi-Lagrangian method. The fourth-order weighted essentially non-oscillatory (4th WENO) limiter is applied to the first derivative value to minimize numerical oscillation in the discharge oscillation analyses. The fourth-order accuracy is verified through a 1D scalar test case. Nonoscillatory and high-res

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Yang, Yue, and D. I. Pullin. "Evolution of vortex-surface fields in viscous Taylor–Green and Kida–Pelz flows." Journal of Fluid Mechanics 685 (October 6, 2011): 146–64. http://dx.doi.org/10.1017/jfm.2011.287.

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AbstractIn order to investigate continuous vortex dynamics based on a Lagrangian-like formulation, we develop a theoretical framework and a numerical method for computation of the evolution of a vortex-surface field (VSF) in viscous incompressible flows with simple topology and geometry. Equations describing the continuous, timewise evolution of a VSF from an existing VSF at an initial time are first reviewed. Non-uniqueness in this formulation is resolved by the introduction of a pseudo-time and a corresponding pseudo-evolution in which the evolved field is ‘advected’ by frozen vorticity onto

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Gong, Zhibin, Jie Li, Jixiang Shan, and Heng Zhang. "Numerical Investigation of Powered Jet Effects by RANS/LES Hybrid Methods." Xibei Gongye Daxue Xuebao/Journal of Northwestern Polytechnical University 37, no. 3 (2019): 565–71. http://dx.doi.org/10.1051/jnwpu/20193730565.

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For the high-precision simulation of engine jet effects, an improved delayed detached eddy simulation (IDDES) method based on the two-equation shear stress transport (SST) model is developed, and the fifth-order finite-volume weighted essentially non-oscillatory (WENO) scheme is employed to enhance accuracy of spatial discretization, and then numerical investigation of powered jet effects by RANS/LES hybrid methods is carried out. The effects of the grid distributions and the accuracy of the spatial schemes are discussed during the RANS/LES validation analysis on the fully expanded jet flow an

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Liu, Zhuoran, Caizheng Wang, Ke Zhang, Zhuo Zhao, and Zhifeng Xie. "Research on Computational Method of Supersonic Inlet/Isolator Internal Flow." Applied Sciences 11, no. 19 (2021): 9272. http://dx.doi.org/10.3390/app11199272.

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In this research, a CFD solver is developed for solving the 2D/3D compressible flow problem: the finite volume method based on multi-block structural grids is used to solve the compressible Reynolds averaged Navier–Stokes equations (RANS). Included in the methodology are multiple high-order reconstruction schemes, such as the 3rd-order MUSCL (Monotone Upstreamcentered Schemes for Conservation Laws), 5th-order WENO (Weight Essentially Non-Oscillatory), and 5th-order MP (Monotonicity-Preserving) schemes. Of the variety of turbulence models that are embedded, this solver is mainly based on the sh

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Chella, Mayilvahanan Alagan, and Hans Bihs. "NUMERICAL MODELLING OF KINEMATICS AND DYNAMICS OF SPILLING AND PLUNGING BREAKERS IN SHALLOW WATERS." Coastal Engineering Proceedings, no. 36 (December 30, 2018): 4. http://dx.doi.org/10.9753/icce.v36.waves.4.

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Wave breaking is a complex two-phase flow process that strongly influences the air-water interaction. A number of physical processes are involved in the exchange of mass, momentum and energy between air and water interaction during the wave breaking process. In shallow waters, waves undergo different transformation processes such as shoaling, refraction, diffraction and breaking due to their non-linear interaction with the seabed. Thus, the associated hydrodynamics are rather complicated to understand when compared to wave breaking in deep water (Lin, 2008). In the present numerical study, a t

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Wang, Cheng, Wen-Hu Han, Yong Bi, and Jian-Xu Ding. "Numerical investigations on reignition behavior of detonation diffraction." Modern Physics Letters B 30, no. 05 (2016): 1650042. http://dx.doi.org/10.1142/s0217984916500421.

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In this paper, by adopting a fifth-order weighted essentially non-oscillatory (WENO) scheme with a third-order TVD Runge–Kutta time stepping method for two-dimensional reactive Euler equations, a parallel code is developed, and reignition behavior after a self-sustaining detonation from the tube into free space filled with H2/O2 mixtures is investigated. The numerical results show that the initial pressure has a great influence on the detonation cellular width, and that as the initial pressure increases, the cellular width gradually decreases and the cellular shape changes from irregular struc

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BURDULEA, Ilinca-Laura, and Alina BOGOI. "Some aspects in Kelvin-Helmholtz instability with and without Boussinesq approximation." INCAS BULLETIN 13, no. 4 (2021): 25–33. http://dx.doi.org/10.13111/2066-8201.2021.13.4.3.

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The topic of this paper is the Kelvin-Helmholtz instability, a phenomenon which occurs on the interface of a stratified fluid, in the presence of a parallel shear flow, when there is a velocity and density difference across the interface of two adjacent layers. This paper focuses on a numerical simulation modelled by the Taylor-Goldstein equation, which represents a more realistic case compared to the basic Kelvin-Helmholtz shear flow. The Euler system is solved with new modelled smooth velocity and density profiles at the interface. The flux at cell boundaries is reconstructed by implementing

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Wang, Cheng, Jianxu Ding, Sirui Tan, and Wenhu Han. "High Order Numerical Simulation of Detonation Wave Propagation Through Complex Obstacles with the Inverse Lax-Wendroff Treatment." Communications in Computational Physics 18, no. 5 (2015): 1264–81. http://dx.doi.org/10.4208/cicp.160115.150915a.

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AbstractThe high order inverse Lax-Wendroff (ILW) procedure is extended to boundary treatment involving complex geometries on a Cartesian mesh. Our method ensures that the numerical resolution at the vicinity of the boundary and the inner domain keeps the fifth order accuracy for the system of the reactive Euler equations with the two-step reaction model. Shock wave propagation in a tube with an array of rectangular grooves is first numerically simulated by combining a fifth order weighted essentially non-oscillatory (WENO) scheme and the ILW boundary treatment. Compared with the experimental

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Dou, Hua-Shu, Zongmin Hu, Boo Cheong Khoo, and Zonglin Jiang. "Numerical Simulation of Deflagration to Detonation Transition in a Straight Duct: Effects of Energy Release and Detonation Stability." Advances in Applied Mathematics and Mechanics 6, no. 06 (2014): 718–31. http://dx.doi.org/10.4208/aamm.2013.m159.

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AbstractNumerical simulation based on the Euler equation and one-step reaction model is carried out to investigate the process of deflagration to detonation transition (DDT) occurring in a straight duct. The numerical method used includes a high resolution fifth-order weighted essentially non-oscillatory (WENO) scheme for spatial discretization, coupled with a third order total variation diminishing Runge-Kutta time stepping method. In particular, effect of energy release on the DDT process is studied. The model parameters used are the heat release atq= 50,30,25,20,15,10 and 5, the specific he

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Hegab, A. M., S. A. Gutub, and A. Balabel. "A Developed Numerical Method for Turbulent Unsteady Fluid Flow in Two-Phase Systems with Moving Interface." International Journal of Computational Methods 14, no. 06 (2017): 1750063. http://dx.doi.org/10.1142/s0219876217500633.

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This paper presents the development of an accurate and robust numerical modeling of instability of an interface separating two-phase system, such as liquid–gas and/or solid–gas systems. The instability of the interface can be refereed to the buoyancy and capillary effects in liquid–gas system. The governing unsteady Navier–Stokes along with the stress balance and kinematic conditions at the interface are solved separately in each fluid using the finite-volume approach for the liquid–gas system and the Hamilton–Jacobi equation for the solid–gas phase. The developed numerical model represents th

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Singh, Paramjeet, Santosh Kumar, and Mehmet Emir Koksal. "High-order finite volume approximation for population density model based on quadratic integrate-and-fire neuron." Engineering Computations 36, no. 1 (2018): 84–102. http://dx.doi.org/10.1108/ec-11-2017-0445.

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PurposeThe purpose of this paper is to develop and apply a high-order numerical method based on finite volume approximation for quadratic integrate-and-fire (QIF) neuron model with the help of population density approach.Design/methodology/approachThe authors apply the population density approach for the QIF neuron model to derive the governing equation. The resulting mathematical model cannot be solved with existing analytical or numerical techniques owing to the presence of delay and advance. The numerical scheme is based along the lines of approximation: spatial discretization is performed

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Karthaus, Meinolf, J. Riesle-Keil, Ursula Weber, and Ingeburg Wolf. "Implementation of an End-of-Life Care Pathway in Cancer Patients." Blood 120, no. 21 (2012): 4689. http://dx.doi.org/10.1182/blood.v120.21.4689.4689.

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Abstract Abstract 4689 Background: Supportive care for dying hemato-oncological patients in the hospital remains an unmet need. The Liverpool Care Pathway (LCP) has been developed in Europe for patients in the final 24–72 h of life to help physicians and nurses in the end-of-life care (ELC). We evaluated appropriately timed cessation of treatment in a Hemato-Oncology Department after integration of a modified LCP in a tertiary Munich cancer center. The End-of-life Care Pathway was modified to suit local conditions. The aim of the trial was to include over 40% of dying patients in the ELC. The

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Fracasso, P. M., R. Govindan, M. J. Ellis, et al. "Phase 1 and pharmacokinetic study of weekly docosahexaenoic acid-paclitaxel (Taxoprexin) in resistant solid tumor malignancies." Journal of Clinical Oncology 24, no. 18_suppl (2006): 2036. http://dx.doi.org/10.1200/jco.2006.24.18_suppl.2036.

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2036 Background: Docosahexaenoic acid-paclitaxel (DHAP) is a covalent conjugate of paclitaxel and the essential fatty acid, docosahexaenoic acid. Preclinical studies have demonstrated increased activity relative to paclitaxel with the potential for an improved therapeutic ratio. We performed a phase 1 and pharmacokinetics (PK) study of DHAP in patients with resistant solid tumor malignancies. Methods: Patients were treated with DHAP administered by 2-hour intravenous infusion weekly for three out of four weeks. Dose escalation started at DHAP 200 mg/m2 and was increased by 100 mg/m2 per dose l

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Pawlyn, Charlotte, Faith E. Davies, Martin F. Kaiser, et al. "Primary IMiD Refractory Myeloma; Results from 3894 Patients Treated in the Phase III Myeloma XI Study." Blood 128, no. 22 (2016): 1144. http://dx.doi.org/10.1182/blood.v128.22.1144.1144.

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Abstract Background Primary refractory myeloma is an important therapeutic challenge; understanding its clinical course and biology is essential if we are to recognize it early and target it therapeutically. Immunomodulatory (IMiD) drugs are widely used as induction therapy with good response rates but a small proportion of patients are refractory. The mechanism underlying IMiD resistance is poorly defined. Mutations in the cereblon pathway are a clear candidate but have not been widely looked for or reported. An important question is whether the primary refractory clone carries class-specific

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Andersen, Harald. "Nu bli’r der ballade." Kuml 50, no. 50 (2001): 7–32. http://dx.doi.org/10.7146/kuml.v50i50.103098.

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We’ll have trouble now!The Archaeological Society of Jutland was founded on Sunday, 11 March 1951. As with most projects with which P.V Glob was involved, this did not pass off without drama. Museum people and amateur archaeologists in large numbers appeared at the Museum of Natural History in Aarhus, which had placed rooms at our disposal. The notable dentist Holger Friis, the uncrowned king of Hjørring, was present, as was Dr Balslev from Aidt, Mr and Mrs Overgaard from Holstebro Museum, and the temperamental leader of Aalborg Historical Museum, Peter Riismøller, with a number of his discipl

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Grischuk, Tatiana. "Symptom. Toxic story." Mental Health: Global Challenges Journal 4, no. 2 (2020): 19–24. http://dx.doi.org/10.32437/mhgcj.v4i2.91.

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Introduction Such symptoms as hard, complex, bodily or mental feelings, that turn our everyday life into a hell, at first, lead us to a doctor, and then - to a psychotherapist. A sick man is keen to get rid of a symptom. A doctor prescribes medication, that is ought to eliminate a symptom. A psychotherapist searches for a reason of the problem that needs to be removed. There is such an idea that a neurotic symptom, in particular, an anxiety - is a pathological (spare or extra) response of a body. It is generally believed that such anxiety doesn’t have some real, objective reasons a

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