Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Errors for calculations of strong shocks using an artificial viscosity and artificial heat flux
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
A general topology Godunov method
Journal of Computational Physics
Numerical experiments on the accuracy of ENO and modified ENO schemes
Journal of Scientific Computing
Vorticity errors in multidimensional Lagrangian codes
Journal of Computational Physics
Momentum advection on a staggered mesh
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
Journal of Computational Physics
ADER: A High-Order Approach for Linear Hyperbolic Systems in 2D
Journal of Scientific Computing
Finite Difference WENO Schemes with Lax--Wendroff-Type Time Discretizations
SIAM Journal on Scientific Computing
On the computation of multi-material flows using ALE formulation
Journal of Computational Physics
ADER schemes for three-dimensional non-linear hyperbolic systems
Journal of Computational Physics
Building Blocks for Arbitrary High Order Discontinuous Galerkin Schemes
Journal of Scientific Computing
A high order ENO conservative Lagrangian type scheme for the compressible Euler equations
Journal of Computational Physics
A Cell-Centered Lagrangian Scheme for Two-Dimensional Compressible Flow Problems
SIAM Journal on Scientific Computing
A high order accurate conservative remapping method on staggered meshes
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
A space-time smooth artificial viscosity method for nonlinear conservation laws
Journal of Computational Physics
Positivity-preserving Lagrangian scheme for multi-material compressible flow
Journal of Computational Physics
Hi-index | 31.47 |
In this paper, we explore the Lax-Wendroff (LW) type time discretization as an alternative procedure to the high order Runge-Kutta time discretization adopted for the high order essentially non-oscillatory (ENO) Lagrangian schemes developed in [3,5]. The LW time discretization is based on a Taylor expansion in time, coupled with a local Cauchy-Kowalewski procedure to utilize the partial differential equation (PDE) repeatedly to convert all time derivatives to spatial derivatives, and then to discretize these spatial derivatives based on high order ENO reconstruction. Extensive numerical examples are presented, for both the second-order spatial discretization using quadrilateral meshes [3] and third-order spatial discretization using curvilinear meshes [5]. Comparing with the Runge-Kutta time discretization procedure, an advantage of the LW time discretization is the apparent saving in computational cost and memory requirement, at least for the two-dimensional Euler equations that we have used in the numerical tests.