Journal of Scientific Computing
A relaxation scheme for the hydrodynamic equations for semiconductors
Applied Numerical Mathematics
ICCS '02 Proceedings of the International Conference on Computational Science-Part II
Kinetic derivation of a finite difference scheme for the incompressible Navier--Stokes equation
Journal of Computational and Applied Mathematics
Future Generation Computer Systems - Special issue: Selected numerical algorithms
Numerical simulation of a generalized Zakharov system
Journal of Computational Physics
Variants of relaxed schemes and two-dimensional gas dynamics
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Implicit---Explicit Runge---Kutta Schemes and Applications to Hyperbolic Systems with Relaxation
Journal of Scientific Computing
A Time-Splitting Spectral Method for the Generalized Zakharov System in Multi-Dimensions
Journal of Scientific Computing
Contractivity/monotonicity for additive Runge-Kutta methods: inner product norms
Applied Numerical Mathematics
Numerical approximation of the viscous quantum hydrodynamic model for semiconductors
Applied Numerical Mathematics
Mathematics and Computers in Simulation - Special issue: Nonlinear waves: computation and theory IV
Numerical methods for solving moment equations in kinetic theory of neuronal network dynamics
Journal of Computational Physics
A modified higher order Godunov's scheme for stiff source conservative hydrodynamics
Journal of Computational Physics
A lattice-Boltzmann relaxation scheme for coupled convection-radiation systems
Journal of Computational Physics
Finite volume schemes of very high order of accuracy for stiff hyperbolic balance laws
Journal of Computational Physics
Journal of Computational Physics
An Asymptotic Preserving scheme for the Euler equations in a strong magnetic field
Journal of Computational Physics
Contractivity/monotonicity for additive Runge--Kutta methods: Inner product norms
Applied Numerical Mathematics
Variants of relaxed schemes and two-dimensional gas dynamics
Journal of Computational and Applied Mathematics - Special issue: Selected papers of the international conference on computational methods in sciences and engineering (ICCMSE-2003)
Mathematics and Computers in Simulation
Journal of Computational Physics
SIAM Journal on Scientific Computing
On Stability, Monotonicity, and Construction of Difference Schemes I: Theory
SIAM Journal on Scientific Computing
On Stability, Monotonicity, and Construction of Difference Schemes II: Applications
SIAM Journal on Scientific Computing
Exponential Runge-Kutta Methods for Stiff Kinetic Equations
SIAM Journal on Numerical Analysis
Applied Numerical Mathematics
Hi-index | 0.04 |
We develop high-resolution shock-capturing numerical schemes for hyperbolic systems with relaxation. In such systems the relaxation time may vary from order-1 to much less than unity. When the relaxation time is small, the relaxation term becomes very strong and highly stiff, and underresolved numerical schemes may produce spurious results. Usually one cannot decouple the problem into separate regimes and handle different regimes with different methods. Thus it is important to have a scheme that works uniformly with respect to the relaxation time. Using the Broadwell model of the nonlinear Boltzmann equation we develop a second-order scheme that works effectively, with a fixed spatial and temporal discretization, for all ranges of the mean free path. Formal uniform consistency proof for a first-order scheme and numerical convergence proof for the second-order scheme are also presented. We also make numerical comparisons of the new scheme with some other schemes. This study is motivated by the reentry problem in hypersonic computations.