Discrete models for the numerical analysis of time-dependent multidimensional gas dynamics
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
Numerical solution of the Riemann problem for two-dimensional gas dynamics
SIAM Journal on Scientific Computing
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Characteristic Galerkin Schemes for Scalar Conservation Laws in Two and Three Space Dimensions
SIAM Journal on Numerical Analysis
On WAF-type schemes for multidimensional hyperbolic conservation laws
Journal of Computational Physics
Wave propagation algorithms for multidimensional hyperbolic systems
Journal of Computational Physics
Multidimensional upwinding. Part I. The method of transport for solving the Euler equations
Journal of Computational Physics
Multidimensional upwinding. Part II. Decomposition of the Euler equations into advection equations
Journal of Computational Physics
On the Analysis of Finite Volume Methods for Evolutionary Problems
SIAM Journal on Numerical Analysis
Evolution Galerkin methods for hyperbolic systems in two space dimensions
Mathematics of Computation
Two-dimensional Riemann solver for Euler equations of gas dynamics
Journal of Computational Physics
Vorticity-Preserving Lax--Wendroff-Type Schemes for the System Wave Equation
SIAM Journal on Scientific Computing
Journal of Computational Physics
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Journal of Computational Physics
A multi-dimensional upwind scheme for solving Euler and Navier-Stokes equations
Journal of Computational Physics
Finite volume evolution Galerkin (FVEG) methods for three-dimensional wave equation system
Applied Numerical Mathematics
Journal of Computational Physics
The finite volume local evolution Galerkin method for solving the hyperbolic conservation laws
Journal of Computational Physics
SIAM Journal on Numerical Analysis
A Three-Dimensional, Unsplit Godunov Method for Scalar Conservation Laws
SIAM Journal on Scientific Computing
Directional Diffusion Regulator (DDR) for some numerical solvers of hyperbolic conservation laws
Journal of Computational Physics
Journal of Computational Physics
Finite volume local evolution Galerkin method for two-dimensional relativistic hydrodynamics
Journal of Computational Physics
Hi-index | 31.49 |
We present new truly multidimensional schemes of higher order within the framework of finite volume evolution Galerkin (FVEG) methods for systems of nonlinear hyperbolic conservation laws. These methods couple a finite volume formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of the multidimensional hyperbolic system, such that all of the infinitely many directions of wave propagation are taken into account. Following our previous results for the wave equation system, we derive approximate evolution operators for the linearized Euler equations. The integrals along the Mach cone and along the cell interfaces are evaluated exactly, as well as by means of numerical quadratures. The influence of these numerical quadratures will be discussed. Second-order resolution is obtained using a conservative piecewise bilinear recovery and the midpoint rule approximation for time integration. We prove error estimates for the finite volume evolution Galerkin scheme for linear systems with constant coefficients. Several numerical experiments for the nonlinear. Euler equations, which confirm the accuracy and good multidimensional behavior of the FVEG schemes, are presented as well.