Weighted essentially non-oscillatory schemes
Journal of Computational Physics
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
The effects of numerical viscosities. I: slowly moving shocks
Journal of Computational Physics
The effect of the formulation of nonlinear terms on aliasing errors in spectral methods
Applied Numerical Mathematics
Total variation diminishing Runge-Kutta schemes
Mathematics of Computation
An efficient shock-capturing algorithm for compressible multicomponent problems
Journal of Computational Physics
A general class of commutative filters for LES in complex geometries
Journal of Computational Physics
Simplified discretization of systems of hyperbolic conservation laws containing advection equations
Journal of Computational Physics
Journal of Computational Physics
Numerical Instablilities in Upwind Methods: Analysis and Cures for the “Carbuncle” Phenomenon
Journal of Computational Physics
Computations of compressible multifluids
Journal of Computational Physics
Finite-volume WENO schemes for three-dimensional conservation laws
Journal of Computational Physics
Higher entropy conservation and numerical stability of compressible turbulence simulations
Journal of Computational Physics
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
Journal of Computational Physics
High order Hybrid central-WENO finite difference scheme for conservation laws
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Stability criteria for hybrid difference methods
Journal of Computational Physics
An improved reconstruction method for compressible flows with low Mach number features
Journal of Computational Physics
On entropy generation and dissipation of kinetic energy in high-resolution shock-capturing schemes
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes, II
Journal of Computational Physics
Generalized conservative approximations of split convective derivative operators
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.45 |
The evolution of high-speed initially laminar multicomponent flows into a turbulent multi-material mixing entity, e.g., in the Richtmyer-Meshkov instability, poses significant challenges for high-fidelity numerical simulations. Although high-order shock- and interface-capturing schemes represent such flows well at early times, the excessive numerical dissipation thereby introduced and the resulting computational cost prevent the resolution of small-scale features. Furthermore, unless special care is taken, shock-capturing schemes generate spurious pressure oscillations at material interfaces where the specific heats ratio varies. To remedy these problems, a solution-adaptive high-order central/shock-capturing finite difference scheme is presented for efficient computations of compressible multi-material flows, including turbulence. A new discontinuity sensor discriminates between smooth and discontinuous regions. The appropriate split form of (energy preserving) central schemes is derived for flows of smoothly varying specific heats ratio, such that spurious pressure oscillations are prevented. High-order accurate weighted essentially non-oscillatory (WENO) schemes are applied only at discontinuities; the standard approach is followed for shocks and contacts, but material discontinuities are treated by interpolating the primitive variables. The hybrid nature of the method allows for efficient and accurate computations of shocks and broadband motions, and is shown to prevent pressure oscillations for varying specific heats ratios. The method is assessed through one-dimensional problems with shocks, sharp interfaces and smooth distributions of specific heats ratio, and the two-dimensional single-mode inviscid and viscous Richtmyer-Meshkov instability with re-shock.