Efficient implementation of essentially non-oscillatory shock-capturing schemes
Journal of Computational Physics
Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
High-order essentially nonsocillatory schemes for Hamilton-Jacobi equations
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
Journal of Computational Physics
An isobaric fix for the overheating problem in multimaterial compressible flows
Journal of Computational Physics
A Boundary Condition Capturing Method for Multiphase Incompressible Flow
Journal of Scientific Computing
A second order primitive preconditioner for solving all speed multi-phase flows
Journal of Computational Physics
Adaptive solution techniques for simulating underwater explosions and implosions
Journal of Computational Physics
A numerical method for the simulation of low Mach number liquid-gas flows
Journal of Computational Physics
Practical animation of compressible flow for shock waves and related phenomena
Proceedings of the 2010 ACM SIGGRAPH/Eurographics Symposium on Computer Animation
An unconditionally stable fully conservative semi-Lagrangian method
Journal of Computational Physics
Numerically stable fluid-structure interactions between compressible flow and solid structures
Journal of Computational Physics
Journal of Computational Physics
An Asymptotic-Preserving all-speed scheme for the Euler and Navier-Stokes equations
Journal of Computational Physics
A Coupled Level Set-Moment of Fluid Method for Incompressible Two-Phase Flows
Journal of Scientific Computing
A low Mach number solver: Enhancing applicability
Journal of Computational Physics
A hybrid Lagrangian-Eulerian formulation for bubble generation and dynamics
Proceedings of the 12th ACM SIGGRAPH/Eurographics Symposium on Computer Animation
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We propose a novel method for alleviating the stringent CFL condition imposed by the sound speed in simulating inviscid compressible flow with shocks, contacts and rarefactions. Our method is based on the pressure evolution equation, so it works for arbitrary equations of state, chemical species etc. and is derived in a straight-forward manner. Similar methods have been proposed in the literature, but the equations they are based on and the details of the methods differ significantly. Notably our method leads to a standard Poisson equation similar to what one would solve for incompressible flow, but has an identity term more similar to a diffusion equation. In the limit as the sound speed goes to infinity, one obtains the Poisson equation for incompressible flow. This makes the method suitable for two-way coupling between compressible and incompressible flows and fully implicit solid-fluid coupling, although both of these applications are left to future work. We present a number of examples to illustrate the quality and behavior of the method in both one and two spatial dimensions, and show that for a low Mach number test case we can use a CFL number of 300 (whereas previous work was only able to use a CFL number of 3 on the same example).