Journal of Computational Physics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
WENO schemes with Lax-Wendroff type time discretizations for Hamilton-Jacobi equations
Journal of Computational and Applied Mathematics
Journal of Scientific Computing
Parallel implementation of 3D global MHD simulations for Earth's magnetosphere
Computers & Mathematics with Applications
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
Efficient implementation of high order inverse Lax-Wendroff boundary treatment for conservation laws
Journal of Computational Physics
Journal of Computational and Applied Mathematics
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In this paper we develop a Lax--Wendroff time discretization procedure for high order finite difference weighted essentially nonoscillatory schemes to solve hyperbolic conservation laws. This is an alternative method for time discretization to the popular TVD Runge--Kutta time discretizations. We explore the possibility in avoiding the local characteristic decompositions or even the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining nonoscillatory properties for problems with strong shocks. As a result, the Lax--Wendroff time discretization procedure is more cost effective than the Runge--Kutta time discretizations for certain problems including two-dimensional Euler systems of compressible gas dynamics.