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Articles de revues sur le sujet « Lax-Friedrichs method »

Auteur : Grafiati

Publié le 9 mars 2023

Mis à jour le 31 juillet 2025

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1

Shampine, L. F. "Two-step Lax–Friedrichs method." Applied Mathematics Letters 18, no. 10 (2005): 1134–36. http://dx.doi.org/10.1016/j.aml.2004.11.007.

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Yu, Simin. "A survey of numerical schemes for transportation equation." E3S Web of Conferences 308 (2021): 01020. http://dx.doi.org/10.1051/e3sconf/202130801020.

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The convection-diffusion equation is a fundamental equation that exists widely. The convection-diffusion equation consists of two processes: diffusion and convection. The convection-diffusion equation can also be called drift-diffusion equaintion. The convection – diffusion equation mainly characterizes natural phenomenon in which physical particles, energy are transferred in a system. The well-known linear transport equation is also one kind of convection-diffusion equation. The transport equation can describe the transport of a scalar field such as material feature, chemical reaction or temp

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Breuß, Michael. "The correct use of the Lax–Friedrichs method." ESAIM: Mathematical Modelling and Numerical Analysis 38, no. 3 (2004): 519–40. http://dx.doi.org/10.1051/m2an:2004027.

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Sharma, Deepika, and Kavita Goyal. "Wavelet optimized upwind conservative method for traffic flow problems." International Journal of Modern Physics C 31, no. 06 (2020): 2050086. http://dx.doi.org/10.1142/s0129183120500862.

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Numerical schemes, namely, upwind nonconservative, upwind conservative, Lax–Friedrichs, Lax–Wendroff, MacCormack and Godunov are applied and compared on traffic flow problems. The best scheme, namely, upwind conservative is used for wavelet-optimized method using Daubechies wavelet for numerically solving the same traffic flow problems. Numerical results corresponding to the traffic flow problem with the help of wavelet-optimized, adaptive grid, upwind conservative method have been given. Moreover, the run time carried out by the developed technique have been compared to that of run time carri

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КУЛИКОВ, И. М., та Д. А. КАРАВАЕВ. "ИСПОЛЬЗОВАНИЕ СХЕМЫ ЛАКСА-ФРИДРИХСА С МАЛОЙ ДИССИПАЦИЕЙ ДЛЯ МОДЕЛИРОВАНИЯ РЕЛЯТИВИСТСКИХ ТЕЧЕНИЙ ГАЗА". Сибирский журнал вычислительной математики 26, № 4 (2023): 389–400. http://dx.doi.org/10.15372/sjnm20230404.

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Схема Лакса-Фридрихса традиционно является альтернативой схеме Годунова, так как не требует решения задачи Римана. Использование в случае уравнений специальной релятивистской гидродинамики в схемах Рое, Русанова и в семействе схем Хартена-Лакса-Ван Леера естественного ограничения скорости распространения волн скоростью света приводит нас к конструкции, эквивалентной схеме Лакса-Фридрихса. Важнейшим свойством схемы является ее абсолютная робастность, компенсируемая повышенной диссипативностью. В работе мы предлагаем использовать кусочно-параболическую реконструкцию физических переменных, что по

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Chatterjee, N., and U. S. Fjordholm. "A convergent finite volume method for the Kuramoto equation and related nonlocal conservation laws." IMA Journal of Numerical Analysis 40, no. 1 (2018): 405–21. http://dx.doi.org/10.1093/imanum/dry074.

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Abstract We derive and study a Lax–Friedrichs-type finite volume method for a large class of nonlocal continuity equations in multiple dimensions. We prove that the method converges weakly to the measure-valued solution and converges strongly if the initial data is of bounded variation. Several numerical examples for the kinetic Kuramoto equation are provided, demonstrating that the method works well for both regular and singular data.

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Araujo, Isamara L. N., Panters Rodríguez-Bermúdez, and Yoisell Rodríguez-Núñez. "Numerical Study for Two-Phase Flow with Gravity in Homogeneous and Piecewise-Homogeneous Porous Media." TEMA (São Carlos) 21, no. 1 (2020): 21. http://dx.doi.org/10.5540/tema.2020.021.01.21.

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In this work we study two-phase flow with gravity either in 1-rock homogeneous media or 2-rocks composed media, this phenomenon can be modeled by a non-linear scalar conservation law with continuous flux function or discontinuous flux function, respectively. Our study is essentially from a numerical point of view, we apply the new Lagrangian-Eulerian finite difference method developed by Abreu and Pérez and the Lax-Friedrichs classic method to obtain numerical entropic solutions. Comparisons between numerical and analytical solutions show the efficiency of the methods even for discontinuous fl

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Yu, Kangning, Wenxia Xu, Jibin Yang, Shuo Li, and Guodong Li. "The Limits of Riemann Solutions for Chaplygin Gas Magnetohydrodynamics Euler Equations with Active Terms." Symmetry 17, no. 1 (2025): 77. https://doi.org/10.3390/sym17010077.

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Chaplygin gas magnetohydrodynamics Euler equations with active terms are often used to study physical phenomena in the universe, which is of great significance for exploring unknown fields. This article mainly studies the limited behavior of Riemann solutions of Chaplygin gas magnetohydrodynamics Euler equations with active terms using methods such as the characteristic line method and the Lax–Friedrichs method. In cases where only the magnetic field disappears, it was found, using the characteristic line method, that the solution converges to Chaplygin gas magnetohydrodynamics Euler equations

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Wang, Min, and Xiaohua Zhang. "A High–Order WENO Scheme Based on Different Numerical Fluxes for the Savage–Hutter Equations." Mathematics 10, no. 9 (2022): 1482. http://dx.doi.org/10.3390/math10091482.

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The study of rapid free surface granular avalanche flows has attracted much attention in recent years, which is widely modeled using the Savage–Hutter equations. The model is closely related to shallow water equations. We employ a high-order shock-capturing numerical model based on the weighted essential non-oscillatory (WENO) reconstruction method for solving Savage–Hutter equations. Three numerical fluxes, i.e., Lax–Friedrichs (LF), Harten–Lax–van Leer (HLL), and HLL contact (HLLC) numerical fluxes, are considered with the WENO finite volume method and TVD Runge–Kutta time discretization for

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Ali, Ali Hasan, Ahmed Shawki Jaber, Mustafa T. Yaseen, Mohammed Rasheed, Omer Bazighifan, and Taher A. Nofal. "A Comparison of Finite Difference and Finite Volume Methods with Numerical Simulations: Burgers Equation Model." Complexity 2022 (June 27, 2022): 1–9. http://dx.doi.org/10.1155/2022/9367638.

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In this paper, we present an intensive investigation of the finite volume method (FVM) compared to the finite difference methods (FDMs). In order to show the main difference in the way of approaching the solution, we take the Burgers equation and the Buckley–Leverett equation as examples to simulate the previously mentioned methods. On the one hand, we simulate the results of the finite difference methods using the schemes of Lax–Friedrichs and Lax–Wendroff. On the other hand, we apply Godunov’s scheme to simulate the results of the finite volume method. Moreover, we show how starting with a v

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Puja Negara, Teguh, Hendradi Hardhienata, and Husin Alatas. "Simulation of Electromagnetic Wave Propagation in Graphene-Coated 1D Photonic Crystals Using the Finite Volume Method." Journal of Physics: Conference Series 2973, no. 1 (2025): 012012. https://doi.org/10.1088/1742-6596/2973/1/012012.

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Abstract A numerical study on the interaction of electromagnetic waves with photonic crystals with one-dimensional periodicity has been carried out using the Finite Volume method. The photonic crystals with one-dimensional periodicity consists of 7 alternating layers of SiO2 and GaAs with thicknesses of 1.55 μm and 3.10 μm, respectively. Electromagnetic field components have been simulated to propagate through the photonic crystal structure, experiencing reflection and transmission at each layer of the structure. The simulation results show the occurrence of absorption precisely at the Bragg f

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Setiyowati, R., and Sumardi. "A Simulation of Shallow Water Wave Equation Using Finite Volume Method: Lax-Friedrichs Scheme." Journal of Physics: Conference Series 1306 (August 2019): 012022. http://dx.doi.org/10.1088/1742-6596/1306/1/012022.

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Kao, Chiu Yen, Carmeliza Navasca, and Stanley Osher. "The Lax–Friedrichs sweeping method for optimal control problems in continuous and hybrid dynamics." Nonlinear Analysis: Theory, Methods & Applications 63, no. 5-7 (2005): e1561-e1572. http://dx.doi.org/10.1016/j.na.2005.01.061.

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Arry Sanjoyo, Bandung, Mochamad Hariadi, and Mauridhi Hery Purnomo. "Stable Algorithm Based On Lax-Friedrichs Scheme for Visual Simulation of Shallow Water." EMITTER International Journal of Engineering Technology 8, no. 1 (2020): 19–34. http://dx.doi.org/10.24003/emitter.v8i1.479.

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Many game applications require fluid flow visualization of shallow water, especially dam-break flow. A Shallow Water Equation (SWE) is a mathematical model of shallow water flow which can be used to compute the flow depth and velocity. We propose a stable algorithm for visualization of dam-break flow on flat and flat with bumps topography. We choose Lax-Friedrichs scheme as the numerical method for solving the SWE. Then, we investigate the consistency, stability, and convergence of the scheme. Finally, we transform the strategy into a visualization algorithm of SWE and analyze the complexity.

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Dinh Dung, NGUYEN. "LAX - FRIEDRICHS REGULARIZATION DIFFERENCE ALGORITHM FOR TRAFFIC DENSITY FORECASTING PROBLEM WITH DELAY." Vinh University Journal of Science 53, no. 1A (2023): 54–60. http://dx.doi.org/10.56824/vujs.2023a144.

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In recent years, traffic density forecasting has been playing an important role in developing and improving the performance of intelligent traffic systems. Traffic density forecasting to optimize traffic management, urban management of vehicular traffic have the ability to coordinate traffic, optimize traffic light signals and apply intelligent regulation based on forecasts, thereby improving the handling of the road segment and reducing travel time. Therefore, the construction of predictive algorithms along with integration into traffic management systems is essential to promote the sustainab

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Krasnov, Mikhail Mikhailovich, Marina Eugenievna Ladonkina, Olga Alexandrovna Neklyudova, and Vladimir Fedorovich Tishkin. "On the influence of the choice of the numerical flow on the solution of problems with shock waves by the discontinuous Galerkin method." Keldysh Institute Preprints, no. 91 (2022): 1–21. http://dx.doi.org/10.20948/prepr-2022-91.

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The paper compares various numerical flows in the calculation of flows with the presence of shock waves by first-order schemes and second-order DG method on schemes from the Quirk’s list, namely: the Quirk problem and its modifications, shock wave diffraction at a 90 degree angle, the problem of double Mach reflection. It is shown that the use of HLLC and Godunov’s numerical flows in calculations can lead to instability, the Rusanov-Lax-Friedrichs flow leads to high dissipation of the calculation. The most versatile in carrying out production calculations are hybrid numerical flows, which allo

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Rossi, Elena, Jennifer Weißen, Paola Goatin, and Simone Göttlich. "Well-posedness of a non-local model for material flow on conveyor belts." ESAIM: Mathematical Modelling and Numerical Analysis 54, no. 2 (2020): 679–704. http://dx.doi.org/10.1051/m2an/2019062.

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In this paper, we focus on finite volume approximation schemes to solve a non-local material flow model in two space dimensions. Based on the numerical discretisation with dimensional splitting, we prove the convergence of the approximate solutions, where the main difficulty arises in the treatment of the discontinuity occurring in the flux function. In particular, we compare a Roe-type scheme to the well-established Lax–Friedrichs method and provide a numerical study highlighting the benefits of the Roe discretisation. Besides, we also prove the L1-Lipschitz continuous dependence on the initi

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Xu, J., M. Luo, Z. Wu, S. Wang, B. Qi, and Z. Qiao. "Pressure and Temperature Prediction of Transient Flow in HTHP Injection Wells by Lax-Friedrichs Method." Petroleum Science and Technology 31, no. 9 (2013): 960–76. http://dx.doi.org/10.1080/10916466.2010.535083.

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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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Vosoughifar, Hamid Reza, Azam Dolatshah, and Seyed Kazem Sadat Shokouhi. "Discretization of Multidimensional Mathematical Equations of Dam Break Phenomena Using a Novel Approach of Finite Volume Method." Journal of Applied Mathematics 2013 (2013): 1–12. http://dx.doi.org/10.1155/2013/642485.

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This paper was concerned to simulate both wet and dry bed dam break problems. A high-resolution finite volume method (FVM) was employed to solve the one-dimensional (1D) and two-dimensional (2D) shallow water equations (SWEs) using an unstructured Voronoi mesh grid. In this attempt, the robust local Lax-Friedrichs (LLxF) scheme was used for the calculating of the numerical flux at cells interfaces. The model named V-Break was run under the asymmetry partial and circular dam break conditions and then verified by comparing the model outputs with the documented results. Due to a precise agreement

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Wang, Shu, and Yabo Ren. "Weak solutions to the Cauchy problem of the time-dependent Thomas–Fermi equations." Journal of Mathematical Physics 63, no. 6 (2022): 061507. http://dx.doi.org/10.1063/5.0082846.

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In this paper, we are concerned with the existence of weak solutions of the time-dependent Thomas–Fermi equations. We derive approximate solutions by the fractional step Lax–Friedrichs scheme and establish uniform boundedness of approximate solutions. Based on the uniform energy-type estimates, we establish that the entropy dissipation measures of the weak solution of the one-dimensional time-dependent Thomas–Fermi equations for weak entropy–entropy flux pairs, generated by compactly supported [Formula: see text] test functions, are confined in a compact set in [Formula: see text]. We prove th

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Tishkin, V. F., and M. E. Ladonkina. "The Discontinuous Galerkin Method and its Implementation in the RAMEG3D Software Package." Computational Mathematics and Information Technologies 7, no. 2 (2023): 7–18. http://dx.doi.org/10.23947/2587-8999-2023-7-2-7-18.

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Currently, the Discontinuous Galerkin Method (DGM) is widely used to solve complex multi-scale problems of mathematical physics that have important applied significance. When implementing it, the question of choosing a discrete approximation of flows for viscous terms of the Navier-Stokes equation is important.It is necessary to focus on the construction of limiting functions, on the selection of the best discrete approximations of diffusion flows, and on the use of implicit and iterative methods for solving the obtained differential-difference equations for the successful application of DGM o

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Outada, Nisrine, Nicolas Vauchelet, Thami Akrid, and Mohamed Khaladi. "From kinetic theory of multicellular systems to hyperbolic tissue equations: Asymptotic limits and computing." Mathematical Models and Methods in Applied Sciences 26, no. 14 (2016): 2709–34. http://dx.doi.org/10.1142/s0218202516500640.

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This paper deals with the analysis of the asymptotic limit toward the derivation of macroscopic equations for a class of equations modeling complex multicellular systems by methods of the kinetic theory. After having chosen an appropriate scaling of time and space, a Chapman–Enskog expansion is combined with a closed, by minimization, technique to derive hyperbolic models at the macroscopic level. The resulting macroscopic equations show how the macroscopic tissue behavior can be described by hyperbolic systems which seem the most natural in this context. We propose also an asymptotic-preservi

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Zhou, Shengcheng, Zhipeng Li, and Li Deng. "Spatial convergence study of Lax-Friedrichs WENO fast sweeping method on the SN transport equation with nonsmoothness." Annals of Nuclear Energy 166 (February 2022): 108707. http://dx.doi.org/10.1016/j.anucene.2021.108707.

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Mohamed, Kamel, Hanan A. Alkhidhr, and Mahmoud A. E. Abdelrahman. "The NHRS scheme for the Chaplygin gas model in one and two dimensions." AIMS Mathematics 7, no. 10 (2022): 17785–801. http://dx.doi.org/10.3934/math.2022979.

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<abstract><p>The main motive of this work is to introduce a numerical investigation for the one and two-dimensional (1D/2D) Chaplygin gas model. Namely, we developed the non homogeneous Riemann solver (NHRS) method to solve these models. After discussing the Chaplygin gas models and the numerical scheme, various 1D and 2D test problems are introduced. In order to complete the numerical investigation in a completely unified way, Rusanov scheme, modified Lax-Friedrichs and analytical solution are compared with NHRS scheme in 1D case. The acquired results clarify the high resolution o

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Xu, Jiuping, Min Luo, Jiancheng Hu, Shize Wang, Bin Qi, and Zhiguo Qiao. "A Direct Eulerian GRP Scheme for the Prediction of Gas-Liquid Two-Phase Flow in HTHP Transient Wells." Abstract and Applied Analysis 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/171732.

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A coupled system model of partial differential equations is presented in this paper, which concerns the variation of the pressure and temperature, velocity, and density at different times and depths in high temperature-high pressure (HTHP) gas-liquid two-phase flow wells. A new dimensional splitting technique with Eulerian generalized riemann problem (GRP) scheme is applied to solve this set of conservation equations, where Riemann invariants are introduced as the main ingredient to resolve the generalized Riemann problem. The basic data of “X well” (HTHP well), 7100 m deep, located in Southwe

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Martínez-Aranda, S., A. Ramos-Pérez, and P. García-Navarro. "A 1D shallow-flow model for two-layer flows based on FORCE scheme with wet–dry treatment." Journal of Hydroinformatics 22, no. 5 (2020): 1015–37. http://dx.doi.org/10.2166/hydro.2020.002.

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Abstract The two-layer problem is defined as the coexistence of two immiscible fluids, separated by an interface surface. Under the shallow-flow hypothesis, 1D models are based on a four equations system accounting for the mass and momentum conservation in each fluid layer. Mathematically, the system of conservation laws modelling 1D two-layer flows has the important drawback of loss of hyperbolicity, causing that numerical schemes based on the eigenvalues of the Jacobian become unstable. In this work, well-balanced FORCE scheme is proposed for 1D two-layer shallow flows. The FORCE scheme comb

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Hong, Chengyu, Xuben Wang, Gaishan Zhao, et al. "Discontinuous finite element method for efficient three-dimensional elastic wave simulation." Journal of Geophysics and Engineering 18, no. 1 (2021): 98–112. http://dx.doi.org/10.1093/jge/gxaa070.

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Abstract The existing discontinuous Galerkin (DG) finite element method (FEM) for the numerical simulation of elastic wave propagation is primarily implemented in two dimensions. Here, a discontinuous FEM (DFEM) for efficient three-dimensional (3D) elastic wave simulation is presented. First, the velocity–stress equations of 3D elastic waves in isotropic media are transformed into first-order coefficient-changed partial differential equations. A DG discretisation method for wave field values on a unit boundary is then defined using the local Lax–Friedrichs flux format. The equations are first

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Amundsen, Lasse, and Ørjan Pedersen. "Time step n-tupling for wave equations." GEOPHYSICS 82, no. 6 (2017): T249—T254. http://dx.doi.org/10.1190/geo2017-0377.1.

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We have constructed novel temporal discretizations for wave equations. We first select an explicit time integrator that is of second order, leading to classic time marching schemes in which the next value of the wavefield at the discrete time [Formula: see text] is computed from current values known at time [Formula: see text] and the previous time [Formula: see text]. Then, we determine how the time step can be doubled, tripled, or generally, [Formula: see text]-tupled, producing a new time-stepping method in which the next value of the wavefield at the discrete time [Formula: see text] is co

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Palm, Johannes, and Claes Eskilsson. "Influence of Bending Stiffness on Snap Loads in Marine Cables: A Study Using a High-Order Discontinuous Galerkin Method." Journal of Marine Science and Engineering 8, no. 10 (2020): 795. http://dx.doi.org/10.3390/jmse8100795.

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Marine cables are primarily designed to support axial loads. The effect of bending stiffness on the cable response is therefore often neglected in numerical analysis. However, in low-tension applications such as umbilical modelling of ROVs or during slack events, the bending forces may affect the slack regime dynamics of the cable. In this paper, we present the implementation of bending stiffness as a rotation-free, nested local Discontinuous Galerkin (DG) method into an existing Lax–Friedrichs-type solver for cable dynamics based on an hp-adaptive DG method. Numerical verification shows expon

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Hu, Jiangtao, Jianliang Qian, Jian Song, Min Ouyang, Junxing Cao, and Shingyu Leung. "Eulerian partial-differential-equation methods for complex-valued eikonals in attenuating media." GEOPHYSICS 86, no. 4 (2021): T179—T192. http://dx.doi.org/10.1190/geo2020-0659.1.

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Seismic waves in earth media usually undergo attenuation, causing energy losses and phase distortions. In the regime of high-frequency asymptotics, a complex-valued eikonal is an essential ingredient for describing wave propagation in attenuating media, where the real and imaginary parts of the eikonal function capture dispersion effects and amplitude attenuation of seismic waves, respectively. Conventionally, such a complex-valued eikonal is mainly computed either by tracing rays exactly in complex space or by tracing rays approximately in real space so that the resulting eikonal is distribut

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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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Keshari, Ashok K., Deba P. Satapathy, and Amod Kumar. "The influence of vertical density and velocity distributions on snow avalanche runout." Annals of Glaciology 51, no. 54 (2010): 200–206. http://dx.doi.org/10.3189/172756410791386409.

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AbstractA one-dimensional avalanche dynamics model accounting for vertical density and velocity distributions is presented. Mass and momentum flux distribution factors are derived to incorporate the effect of density and velocity variations within the framework of depth-integrated models. Using experiments of avalanche flows on an inclined snow chute at Dhundhi, Manali, India, we conceptualize snow flow rheology as a Voellmy fluid where the distribution of internal shearing is given by a Newtonian fluid (NF) or Criminale–Ericksen–Filbey fluid (CEFF). Then the generalized mass and momentum dist

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Alayachi, H. S., Mahmoud A. E. Abdelrahman, and Kamel Mohamed. "Finite-volume two-step scheme for solving the shear shallow water model." AIMS Mathematics 9, no. 8 (2024): 20118–35. http://dx.doi.org/10.3934/math.2024980.

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<abstract><p>The shear shallow water (SSW) model introduces an approximation for shallow water flows by including the effect of vertical shear in the system. Six non-linear hyperbolic partial differential equations with non-conservative laws make up this system. Shear, contact, rarefaction, and shock waves are all admissible in this model. We developed the finite-volume two-step scheme, the so-called generalized Rusanov (G. Rusanov) scheme, for solving the SSW model. This method is split into two stages. The first one relies on a local parameter that permits control over the diffus

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Mo, Tiexiang, and Guodong Li. "Parallel Accelerated Fifth-Order WENO Scheme-Based Pipeline Transient Flow Solution Model." Applied Sciences 12, no. 14 (2022): 7350. http://dx.doi.org/10.3390/app12147350.

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The water hammer phenomenon is the main problem in long-distance pipeline networks. The MOC (Method of characteristics) and finite difference methods lead to severe constraints on the mesh and Courant number, while the finite volume method of the second-order Godunov scheme has limited intermittent capture capability. These methods will produce severe numerical dissipation, affecting the computational efficiency at low Courant numbers. Based on the lax-Friedrichs flux splitting method, combined with the upstream and downstream virtual grid boundary conditions, this paper uses the high-precisio

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Ariunaa, U., M. Dumbser, and Ts Sarantuya. "Complete Riemann Solvers for the Hyperbolic GPR Model of Continuum Mechanics." Bulletin of Irkutsk State University. Series Mathematics 35 (2021): 60–72. http://dx.doi.org/10.26516/1997-7670.2021.35.60.

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In this paper, complete Riemann solver of Osher-Solomon and the HLLEM Riemann solver for unified first order hyperbolic formulation of continuum mechanics, which describes both of fluid and solid dynamics, are presented. This is the first time that these types of Riemann solvers are applied to such a complex system of governing equations as the GPR model of continuum mechanics. The first order hyperbolic formulation of continuum mechanics recently proposed by Godunov S. K., Peshkov I. M. and Romenski E. I., further denoted as GPR model includes a hyperbolic formulation of heat conduction and a

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Wang, Guofang, Jing Fang, Lulu Jiang, Wang Yao, and Ning Li. "Coupled Alternating Neural Networks for Solving Multi-Population High-Dimensional Mean-Field Games." Mathematics 12, no. 23 (2024): 3803. https://doi.org/10.3390/math12233803.

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Multi-population mean-field game is a critical subclass of mean-field games (MFGs). It is a theoretically feasible multi-agent model for simulating and analyzing the game between multiple heterogeneous populations of interacting massive agents. Due to the factors of game complexity, dimensionality disaster and disturbances should be taken into account simultaneously to solve the multi-population high-dimensional stochastic MFG problem, which is a great challenge. We present CA-Net, a coupled alternating neural network approach for tractably solving multi-population high-dimensional MFGs. First

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Bürger, Raimund, Harold Deivi Contreras, and Luis Miguel Villada. "A Hilliges-Weidlich-type scheme for a one-dimensional scalar conservation law with nonlocal flux." Networks and Heterogeneous Media 18, no. 2 (2023): 664–93. http://dx.doi.org/10.3934/nhm.2023029.

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<abstract><p>The simulation model proposed in [M. Hilliges and W. Weidlich. A phenomenological model for dynamic traffic flow in networks. <italic>Transportation Research Part B: Methodological</italic>, <bold>29</bold> (6): 407–431, 1995] can be understood as a simple method for approximating solutions of scalar conservation laws whose flux is of density times velocity type, where the density and velocity factors are evaluated on neighboring cells. The resulting scheme is monotone and converges to the unique entropy solution of the underlying problem. The s

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Hanh, Nguyen Van, Nguyen Van Diep, and Ngo Huy Can. "On some numerical methods for solving the 1-D Saint-Venant equations of general flow regime. Part 1: Numerical methods." Vietnam Journal of Mechanics 24, no. 4 (2002): 236–48. http://dx.doi.org/10.15625/0866-7136/24/4/6623.

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Development of methods for numerical simulation of dike- or dam-break flood is one of essential problems of Fluid Mechanics at the present time. Many numerical methods for solving the 1-D Saint-Venant equations have been proposed. However, the analysis, the evaluation and the selection of appropriate and efficient methods are interest of many research groups and institutions in the world. The purpose of this paper is to introduce and to evaluate four numerical methods for solving the 1-D homogenous Saint-Venant equations in combination with three approaches of processing source terms. The eval

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Madden, Ian, Simone Marras, and Jenny Suckale. "Leveraging Google's Tensor Processing Units for tsunami-risk mitigation planning in the Pacific Northwest and beyond." Geoscientific Model Development 16, no. 12 (2023): 3479–500. http://dx.doi.org/10.5194/gmd-16-3479-2023.

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Abstract. Tsunami-risk mitigation planning has particular importance for communities like those of the Pacific Northwest, where coastlines are extremely dynamic and a seismically active subduction zone looms large. The challenge does not stop here for risk managers: mitigation options have multiplied since communities have realized the viability and benefits of nature-based solutions. To identify suitable mitigation options for their community, risk managers need the ability to rapidly evaluate several different options through fast and accessible tsunami models, but they may lack high-perform

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Spa, Carlos, Otilio Rojas, and Josep de la Puente. "Comparison of expansion-based explicit time-integration schemes for acoustic wave propagation." GEOPHYSICS 85, no. 3 (2020): T165—T178. http://dx.doi.org/10.1190/geo2019-0462.1.

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We have developed a von Neumann stability and dispersion analysis of two time-integration techniques in the framework of Fourier pseudospectral (PS) discretizations of the second-order wave equation. The first technique is a rapid expansion method (REM) that uses Chebyshev matrix polynomials to approximate the continuous solution operator of the discrete wave equation. The second technique is a Lax-Wendroff method (LWM) that replaces time derivatives in the Taylor expansion of the solution wavefield with their equivalent spatial PS differentiations. In both time-integration schemes, each expan

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Дубровський, І. Д., and В. Л. Бучарський. "THE APPLICATION OF THE EXTENDED CELLS METHOD TO SIMULATE THE FLOW OF COMBUSTION GASES IN THE LPRE CHAMBER." Journal of Rocket-Space Technology 31, no. 4 (2023): 32–39. http://dx.doi.org/10.15421/452305.

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   Abstract. The numerical modeling of the process of two-dimensional axisymmetric flow of combustion gases in the chamber of a liquid rocket engine is considered in this study. In general, when solving such problems, meshes are used which lines coincide with the boundaries of the computational domain. However, an alternative solution is proposed here, which is to apply the extended cells method. It allows using rectangular Cartesian grids, which lines do not coincide with the boundaries of the computational domain, without reducing the stability of the numerical solution due

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Gama, Italon Rilson Vicente, André Luiz Andrade Simões, Harry Edmar Schulz, and Rodrigo De Melo Porto. "CÓDIGO LIVRE PARA SOLUÇÃO NUMÉRICA DAS EQUAÇÕES DE SAINT-VENANT EM CANAIS TRAPEZOIDAIS ASSIMÉTRICOS." Revista Eletrônica de Gestão e Tecnologias Ambientais 8, no. 2 (2020): 145. http://dx.doi.org/10.9771/gesta.v8i2.38913.

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<p>Ondas de cheia em canais e ondas produzidas por manobras em comportas são alguns fenômenos simulados com as equações de Saint-Venant em aplicações de engenharia. Um novo código foi desenvolvido para a solução dessas equações aplicadas a um canal trapezoidal assimétrico, empregando o método de volumes finitos de Lax e Friedrichs. Foi adotada uma linguagem de programação reconhecida por um <em>software</em> livre. Três testes numéricos foram realizados. O primeiro, correspondente à passagem de uma onda de cheia em um canal retangular, apresentou aderência aos resultados obti

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Zhou, Xiaole, Haiqiang Lan, Ling Chen, et al. "An iterative factored topography-dependent eikonal solver for anisotropic media." GEOPHYSICS 86, no. 5 (2021): U121—U134. http://dx.doi.org/10.1190/geo2020-0662.1.

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Accurate and efficient eikonal solvers for heterogeneous media play an important role in many areas of seismology, such as seismic tomography, migration, and earthquake localization. Incorporating seismic anisotropy and complex topography remain a computational challenge for finite-difference eikonal solvers. In recent years, the topography-dependent eikonal equation (TDEE) has been proposed as an effective way to calculate seismic traveltimes for isotropic and anisotropic media with irregular topography. However, the Lax-Friedrichs sweeping method used in previous studies to approximate the v

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Zhalnin, Ruslan V., Victor F. Masyagin, Elizaveta E. Peskova, and Vladimir F. Tishkin. "Modeling the Flow of Multicomponent Reactive Gas on Unstructured Grids." Engineering Technologies and Systems 30, no. 1 (2020): 162–75. http://dx.doi.org/10.15507/2658-4123.030.202001.162-175.

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Introduction. The article deals with mathematical modeling of the subsonic flow of a multicomponent reactive mixture in a flowing chemical reactor. The numerical algorithm is based on the finite volume method; the calculation is performed on unstructured triangular grids using the Message Passing Interface parallel computing technology. Materials and Methods. To describe the flows under studying, the Navier–Stokes equations are used in the approximation for low Mach numbers. To solve these equations, the finite volume method on unstructured triangular grids is used. The study uses a splitting

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Cameron, Maria, Sergey Fomel, and James Sethian. "Time-to-depth conversion and seismic velocity estimation using time-migration velocity." GEOPHYSICS 73, no. 5 (2008): VE205—VE210. http://dx.doi.org/10.1190/1.2967501.

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The objective was to build an efficient algorithm (1) to estimate seismic velocity from time-migration velocity, and (2) to convert time-migrated images to depth. We established theoretical relations between the time-migration velocity and seismic velocity in two and three dimensions using paraxial ray-tracing theory. The relation in two dimensions implies that the conventional Dix velocity is the ratio of the interval seismic velocity and the geometric spreading of image rays. We formulated an inverse problem of finding seismic velocity from the Dix velocity and developed a numerical procedur

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Wang, Yunhao, Jiabao Chen, Yan Wang, Yuhang Zeng, and Shitang Ke. "A WENO-Based Upwind Rotated Lattice Boltzmann Flux Solver with Lower Numerical Dissipation for Simulating Compressible Flows with Contact Discontinuities and Strong Shock Waves." Applied Sciences 14, no. 23 (2024): 11450. https://doi.org/10.3390/app142311450.

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This paper presents a WENO-based upwind rotated lattice Boltzmann flux solver (WENO-URLBFS) in the finite difference framework for simulating compressible flows with contact discontinuities and strong shock waves. In the method, the original rotating lattice Boltzmann flux solver is improved by applying the theoretical solution of the Euler equation in the tangential direction of the cell interface to reconstruct the tangential flux so that the numerical dissipation can be reduced. The fluxes at each interface are evaluated using a weighted summation of lattice Boltzmann solutions in two local

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Mwalimo, Delina Mshai, Mary Wainaina, and Winnie Kaluki. "Mixed Vehicular Traffic Flow Model on an Inclined Multilane Road." International Journal of Innovative Science and Research Technology 5, no. 7 (2020): 331–42. http://dx.doi.org/10.38124/ijisrt20jul276.

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This study outlines the Kerner’s 3 phase traffic flow theory, which states that traffic flow occurs in three phases and these are free flow, synchronized flow and wide moving jam phase. A macroscopic traffic model that is factoring road inclination is developed and its features discussed. By construction of the solution to the Rienmann problem, the model is written in conservative form and solved numerically. Using the Lax-Friedrichs method and going ahead to simulate traffic flow on an inclined multi lane road. The dynamics of traffic flow involving cars(fast moving) and trucks(slow moving) o

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Dallakyan, Gurgen. "Numerical Simulations for Chemotaxis Models." Biomath Communications 6, no. 1 (2019): 16. http://dx.doi.org/10.11145/bmc.2019.04.277.

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In the paper, we study the usage of numerical methods in solution of mathematical models of biological problems. More specifically, Keller-Segel type chemotaxis models are discussed, their numerical solutions by sweep and Lax-Friedrichs methods are obtained and interpreted biologically.

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Coppo, Marco, Claudio Dongiovanni, and Claudio Negri. "Numerical Analysis and Experimental Investigation of a Common Rail-Type Diesel Injector." Journal of Engineering for Gas Turbines and Power 126, no. 4 (2004): 874–85. http://dx.doi.org/10.1115/1.1787502.

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A production common rail-type injector has been investigated via numerical simulation and experimentation. The functioning principle of the injector has been carefully analyzed so as to obtain a mathematical model of the device. A zero-dimensional approach has been used for modeling the injector, thus considering the variables as function of time only. The analysis of the hydraulic part of the injector resulted in the definition of an equivalent hydraulic scheme, on which basis both the equations of continuity in chambers and flow through nozzles were written. The connecting pipe between commo

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