Uniformly high order accurate essentially non-oscillatory schemes, 111
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 study of numerical methods for hyperbolic conservation laws with stiff source terms
Journal of Computational Physics
Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
Weighted essentially non-oscillatory schemes
Journal of Computational Physics
High-resolution conservative algorithms for advection in incompressible flow
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
SIAM Journal on Scientific Computing
Comparison of Several Difference Schemes on 1D and 2D Test Problems for the Euler Equations
SIAM Journal on Scientific Computing
Numerical Simulation of High Mach Number Astrophysical Jets with Radiative Cooling
Journal of Scientific Computing
On the numerical solution of a driven thin film equation
Journal of Computational Physics
Hi-index | 31.45 |
We develop a theoretical tool to examine the properties of numerical schemes for advection equations. To magnify the defects of a scheme we consider a convection-reaction equationu"t+(|u|^q/q)"x=u,u,x@?R,t@?R^+,q1.It is shown that, if a numerical scheme for the advection part is performed with a splitting method, the intrinsic properties of the scheme are magnified and observed easily. From this test we observe that numerical solutions based on the Lax-Friedrichs, the MacCormack and the Lax-Wendroff break down easily. These quite unexpected results indicate that certain undesirable defects of a scheme may grow and destroy the numerical solution completely and hence one need to pay extra caution to deal with reaction dominant systems. On the other hand, some other schemes including WENO, NT and Godunov are more stable and one can obtain more detailed features of them using the test. This phenomenon is also similarly observed under other methods for the reaction part.