Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Numerical computation of internal & external flows: fundamentals of numerical discretization
Numerical computation of internal & external flows: fundamentals of numerical discretization
A new finite variable difference method with application to locally exact numerical scheme
Journal of Computational Physics
Analysis and computation with stratified fluid models
Journal of Computational Physics
Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
SIAM Journal on Numerical Analysis
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
SIAM Journal on Scientific Computing
General Software for Two-Dimensional Nonlinear Partial Differential Equations
ACM Transactions on Mathematical Software (TOMS)
Discrete Kinetic Schemes for Multidimensional Systems of Conservation Laws
SIAM Journal on Numerical Analysis
A class of approximate Riemann solvers and their relation to relaxation schemes
Journal of Computational Physics
Explicit diffusive kinetic schemes for nonlinear degenerate parabolic systems
Mathematics of Computation
| Hi-index | 31.45 |
Using the framework of a new relaxation system, which converts a nonlinear viscous conservation law into a system of linear convection-diffusion equations with nonlinear source terms, a finite variable difference method is developed for nonlinear hyperbolic-parabolic equations. The basic idea is to formulate a finite volume method with an optimum spatial difference, using the Locally Exact Numerical Scheme (LENS), leading to a Finite Variable Difference Method as introduced by Sakai [Katsuhiro Sakai, A new finite variable difference method with application to locally exact numerical scheme, Journal of Computational Physics, 124 (1996) pp. 301-308.], for the linear convection-diffusion equations obtained by using a relaxation system. Source terms are treated with the well-balanced scheme of Jin [Shi Jin, A steady-state capturing method for hyperbolic systems with geometrical source terms, Mathematical Modeling Numerical Analysis, 35 (4) (2001) pp. 631-645]. Bench-mark test problems for scalar and vector conservation laws in one and two dimensions are solved using this new algorithm and the results demonstrate the efficiency of the scheme in capturing the flow features accurately.