Uniformly high order accurate essentially non-oscillatory schemes, 111
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Multidimensional upwind methods for hyperbolic conservation laws
Journal of Computational Physics
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Accurate upwind methods for the Euler equations
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
A high-order Godunov method for multiple condensed phases
Journal of Computational Physics
Flux-corrected transport I. SHASTA, a fluid transport algorithm that works
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Towards the ultimate conservative difference scheme V. A second-order sequel to Godunov's method
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
High resolution schemes for hyperbolic conservation laws
Journal of Computational Physics - Special issue: commenoration of the 30th anniversary
Accurate monotonicity-preserving schemes with Runge-Kutta time stepping
Journal of Computational Physics
Computational Considerations for the Simulation of Shock-Induced Sound
SIAM Journal on Scientific Computing
Journal of Computational Physics
A high-order Eulerian Godunov method for elastic-plastic flow in solids
Journal of Computational Physics
A conservative three-dimensional Eulerian method for coupled solid-fluid shock capturing
Journal of Computational Physics
High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations
Journal of Computational Physics
A high-wavenumber viscosity for high-resolution numerical methods
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Runge--Kutta Discontinuous Galerkin Method Using WENO Limiters
SIAM Journal on Scientific Computing
Numerical Convergence Study of Nearly Incompressible, Inviscid Taylor-Green Vortex Flow
Journal of Scientific Computing
Mapped weighted essentially non-oscillatory schemes: Achieving optimal order near critical points
Journal of Computational Physics
Improving Godunov-type reconstructions for simulation of vortex-dominated flows
Journal of Computational Physics
Short Note: A limiter for PPM that preserves accuracy at smooth extrema
Journal of Computational Physics
An evaluation of the FCT method for high-speed flows on structured overlapping grids
Journal of Computational Physics
Journal of Computational Physics
Piecewise parabolic method on a local stencil for magnetized supersonic turbulence simulation
Journal of Computational Physics
High-order conservative finite difference GLM-MHD schemes for cell-centered MHD
Journal of Computational Physics
A space-time smooth artificial viscosity method for nonlinear conservation laws
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.49 |
The last 20 years have seen a wide variety of high-resolution methods that can compute sharp, oscillation-free compressible flows. Here, we combine a complementary set of these methods together in a nonlinear (hybridized) fashion. Our base method is built on a monotone high-resolution Godunov method, the piece-wise parabolic method (PPM). PPM is combined with WENO methods, which reduce the damping of extrema. We find that the relative efficiency of the WENO methods is enhanced by coupling them with the relatively inexpensive Godunov methods. We accomplish our hybridizations through the use of a bounding principle: the approximation used is bounded by two nonlinearly stable approximations. The essential aspect of the method is to have high-order accurate approximations bounded by two non-oscillatory (nonlinearly stable) approximations. The end result is an accuracy-, monotonicity- and extrema-preserving method. These methods are demonstrated on a variety of flows, with quantitative analysis of the solutions with shocks.