Non-oscillatory central differencing for hyperbolic conservation laws
Journal of Computational Physics
SIAM Journal on Scientific Computing
Numerical methods for hyperbolic conservation laws with stiff relaxation I: spurious solutions
SIAM Journal on Applied Mathematics
Derivatives of eigenvalues and eigenvectors of matrix functions
SIAM Journal on Matrix Analysis and Applications
Runge-Kutta methods for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Numerical schemes for hyperbolic conservation laws with stiff relaxation terms
Journal of Computational Physics
Uniformly Accurate Schemes for Hyperbolic Systems with Relaxation
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Numerical Schemes for Hyperbolic Systems of Conservation Laws with Stiff Diffusive Relaxation
SIAM Journal on Numerical Analysis
MOL solvers for hyperbolic PDEs with source terms
Mathematics and Computers in Simulation - IMACS sponsored special issue on method of lines
Numerical Solutions for Partial Differential Equations: Problem Solving Using Mathematica (with Disk)
Runge--Kutta Solutions of a Hyperbolic Conservation Law with Source Term
SIAM Journal on Scientific Computing
A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations
SIAM Journal on Scientific Computing
Central Differencing Based Numerical Schemes for Hyperbolic Conservation Laws with Relaxation Terms
SIAM Journal on Numerical Analysis
Error Estimates for the Staggered Lax--Friedrichs Scheme on Unstructured Grids
SIAM Journal on Numerical Analysis
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
SIAM Journal on Numerical Analysis
On Monotonicity of Difference Schemes for Computational Physics
SIAM Journal on Scientific Computing
Central Runge--Kutta Schemes for Conservation Laws
SIAM Journal on Scientific Computing
Fourth-Order Nonoscillatory Upwind and Central Schemes for Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
On Stability, Monotonicity, and Construction of Difference Schemes I: Theory
SIAM Journal on Scientific Computing
Applied Numerical Mathematics
| Hi-index | 0.00 |
In this paper, we focus on the application and illustration of the approach developed in part I. This approach is found to be useful in the construction of stable and monotone central difference schemes for hyperbolic systems. A new modification of the central Lax-Friedrichs scheme is developed to be of second-order accuracy. The stability of several versions of the developed central scheme is proved. Necessary conditions for the variational monotonicity of the scheme are found. A monotone piecewise cubic interpolation is used in the central schemes to give an accurate approximation for the model in question. The monotonicity parameter introduced in part I is found to be important. That parameter, along with the Courant-Friedrichs-Lewy (CFL) number, plays a major role in the criteria for monotonicity and stability of the central schemes. The modified scheme is tested on several conservation laws taking a CFL number equal or close to unity, and the scheme is found to be accurate and robust.