Godunov's scheme
View article
An efficient unstructured MUSCL scheme for solving the 2D shallow water equations Open
The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to construct the required values at the midpoint of cell edges in a more …
View article
High Order ADER Schemes for Continuum Mechanics Open
In this paper we first review the development of high order ADER finite volume and ADER discontinuous Galerkin schemes on fixed and moving meshes, since their introduction in 1999 by Toro et al. We show the modern variant of ADER based on …
View article
Construction of modified Godunov-type schemes accurate at any Mach number for the compressible Euler system Open
This paper is composed of three self-consistent sections that can be read independently of each other. In Sec. 1, we define and analyze the low Mach number problem through a linear analysis of a perturbed linear wave equation. Then, we sho…
View article
A Godunov type scheme for a class of LWR traffic flow models with non-local flux Open
We present a Godunov type numerical scheme for a class of scalar conservation laws with non-local flux arising for example in traffic flow models. The proposed scheme delivers more accurate solutions than the widely used Lax-Friedrichs typ…
View article
A simple well-balanced and positive numerical scheme for the shallow-water system Open
International audience
View article
A second order all Mach number IMEX finite volume solver for the three dimensional Euler equations Open
This article deals with the development of a numerical method for the compressible Euler system valid for all Mach numbers: from extremely low to high regimes. In classical fluid dynamic problems, one faces both situations in which the flo…
View article
Non-local multi-class traffic flow models Open
We prove the existence for small times of weak solutions for a class of non-local systems in one space dimension, arising in traffic modeling. We approximate the problem by a Godunov type numerical scheme and we provide uniform ${{\mathbf{…
View article
Hamiltonian and Godunov structures of the Grad hierarchy Open
The time evolution governed by the Boltzmann kinetic equation is compatible with mechanics and thermodynamics. The former compatibility is mathematically expressed in the Hamiltonian and Godunov structures, the latter in the structure of g…
View article
Modelling the Impact of Leaky Barriers with a 1D Godunov-Type Scheme for the Shallow Water Equations Open
There is increasing interest in distributing small-scale interventions across the landscape as an alternative means of reducing flood risk. One such intervention, the leaky barrier, is introduced in channels to slow down high flows and enc…
View article
Convergence of a Godunov scheme for conservation laws with a discontinuous flux lacking the crossing condition Open
We study a scalar conservation law whose flux has a single spatial discontinuity. There are many notions of (entropy) solution, the relevant concept being determined by the application. We focus on the so-called vanishing viscosity solutio…
View article
Compressible simulations of bubble dynamics with central-upwind schemes Open
This paper discusses the implementation of an explicit density-based solver, that utilises the centralupwind schemes for the simulation of cavitating bubble dynamic flows. It is highlighted that, in conjunction with the Monotonic Upstream-…
View article
Performance Evaluation of Various Phase Change Materials for Thermal Energy Storage of A Solar Cooker via Numerical Simulation Open
In this paper, thermal performance of various phase change materials (PCMs) used as thermal energy storage in a solar cooker has been investigated numerically. Heat conduction equations in cylindrical domain are used to model heat transfer…
View article
Capacity drop and traffic control for a second order traffic model Open
In this paper, we illustrate how second order traffic flow models, in our case the Aw-Rascle equations, can be used to reproduce empirical observations such as the capacity drop at merges and solve related optimal control problems. To this…
View article
A New Thermodynamically Compatible Finite Volume Scheme for Magnetohydrodynamics Open
In this paper we propose a novel thermodynamically compatible finite volume\nscheme for the numerical solution of the equations of magnetohydrodynamics\n(MHD) in one and two space dimensions. As shown by Godunov in 1972, the MHD\nsystem ca…
View article
A flux‐vector splitting scheme for the shallow water equations extended to high‐order on unstructured meshes Open
We present a flux vector splitting method for the one and two‐dimensional shallow water equations following the approach first proposed by Toro and Vázquez for the compressible Euler equations. The resulting first‐order schemes turn out to…
View article
A stable finite-volume method for scalar field dark matter Open
We describe and test a family of new numerical methods to solve the Schrödinger equation in self-gravitating systems, e.g. Bose–Einstein condensates or ‘fuzzy’/ultra-light scalar field dark matter. The methods are finite-volume Godunov sch…
View article
Godunov-type upwind flux schemes of the two-dimensional finite volume discrete Boltzmann method Open
A simple unified Godunov-type upwind approach that does not need Riemann solvers for the flux calculation is developed for the finite volume discrete Boltzmann method (FVDBM) on an unstructured cell-centered triangular mesh. With piecewise…
View article
Hydrostatic equilibrium preservation in MHD numerical simulation with stratified atmospheres Open
Context. Many astrophysical processes involving plasma flows are produced in the context of a gravitationally stratified atmosphere in hydrostatic equilibrium, in which strong gradients can exist with gas properties that vary in small regi…
View article
Modified Godunov Method for Multicomponent Flow Simulation Open
The paper deals with the elaboration of the algorithm for multicomponent gas flows simulation in the presence of strong shock waves. In order to deal with strong shock wave properly the exact Riemann solver for multicomponent flow and non-…
View article
Exact solution and the multidimensional Godunov scheme for the acoustic equations Open
The acoustic equations derived as a linearization of the Euler equations are a valuable system for studies of multi-dimensional solutions. Additionally they possess a low Mach number limit analogous to that of the Euler equations. Aiming a…
View article
A Macroscopic Traffic Model Based on the Safe Velocity at Transitions Open
The increasing volume of vehicles on the road has had a significant impact on traffic flow. Congestion in urban areas is now a major concern. To mitigate congestion, an accurate model is required which is based on realistic traffic dynamic…
View article
Approximate Riemann solvers for the cosmic ray magnetohydrodynamical equations Open
We analyze the cosmic-ray magnetohydrodynamic (CR MHD) equations to improve\nthe numerical simulations. We propose to solve them in the fully conservation\nform, which is equivalent to the conventional CR MHD equations. In the fully\nconse…
View article
Improved multislope MUSCL reconstruction on unstructured grids for shallow water equations Open
Summary In shallow water flow and transport modeling, the monotonic upstream‐centered scheme for conservation laws (MUSCL) is widely used to extend the original Godunov scheme to second‐order accuracy. The most important step in MUSCL‐type…
View article
Problems of numerical modeling on the basis of some modifications of the Godunov’s scheme Open
The paper verifies the ability of previously proposed modifications of the Godunov's scheme develop physically justified numerical solutions of the inviscid gas dynamics equations.The modifications constructed using the approach proposed b…
View article
An explicit iterative scheme for 3D multicomponent heat conducting flow simulation Open
This paper presents the development and testing of time integration scheme for the system of hydrodynamic equations of gas mixture. These equations take into account the phenomena of multicomponent diffusion and heat transfer. The governin…
View article
A HIGH-RESOLUTION VAN LEER-TYPE SCHEME FOR A MODEL OF FLUID FLOWS IN A NOZZLE WITH VARIABLE CROSS-SECTION Open
We present a high-resolution van Leer-type numerical scheme for the isentropic model of fluid flows in a nozzle with variable cross-section. Basically, the scheme is an improvement of the Godunov-type scheme. The scheme is shown to be well…
View article
Boundary Control Design for Traffic With Nonlinear Dynamics Open
International audience
View article
Numerical investigation on burning rate of propane-air mixture Open
The paper presents a physico-mathematical model and calculation of the burning rate of a propane-air mixture. The problem formulation includes the equations of mass, momentum and energy conservation for the gas, supplemented by the equatio…
View article
A Godunov‐type finite‐volume solver for nonhydrostatic <span>E</span>uler equations with a time‐splitting approach Open
A two‐dimensional conservative nonhydrostatic (NH) model based on the compressible Euler system has been developed in the Cartesian ( x , z ) domain. The spatial discretization is based on a Godunov‐type finite‐volume (FV) method employing…
View article
Two algorithms for a fully coupled and consistently macroscopic PDE-ODEsystem modeling a moving bottleneck on a road Open
In this paper we propose two numerical algorithms to solve a coupled PDE-ODE system which models a slow vehicle (bottleneck) moving on a road together with other cars. The resulting system is fully coupled because the dynamics of the slow …