Boltzmann type schemes for gas dynamics and the entropy property
SIAM Journal on Numerical Analysis
On Godunov-type methods near low densities
Journal of Computational Physics
Second-order Boltzmann schemes for compressible Euler equations in one and two space dimensions
SIAM Journal on Numerical Analysis
Vorticity errors in multidimensional Lagrangian codes
Journal of Computational Physics
On Godunov-type schemes for Lagrangian gas dynamics
SIAM Journal on Numerical Analysis
Efficient implementation of weighted ENO schemes
Journal of Computational Physics
High-Order Positivity-Preserving Kinetic Schemes for the Compressible Euler Equations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
On the Choice of Wavespeeds for the HLLC Riemann Solver
SIAM Journal on Scientific Computing
The construction of compatible hydrodynamics algorithms utilizing conservation of total energy
Journal of Computational Physics
Gas-kinetic schemes for the compressible Euler equations: positivity-preserving analysis
Zeitschrift für Angewandte Mathematik und Physik (ZAMP)
An entropic solver for ideal lagrangian magnetohydrodynamics
Journal of Computational Physics
A Simple Method for Compressible Multifluid Flows
SIAM Journal on Scientific Computing
A fluid-mixture type algorithm for barotropic two-fluid flow problems
Journal of Computational Physics
A high order ENO conservative Lagrangian type scheme for the compressible Euler equations
Journal of Computational Physics
A high order accurate conservative remapping method on staggered meshes
Applied Numerical Mathematics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Journal of Computational Physics
Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
Journal of Computational Physics
Hi-index | 31.45 |
Robustness of numerical methods has attracted an increasing interest in the community of computational fluid dynamics. One mathematical aspect of robustness for numerical methods is the positivity-preserving property. At high Mach numbers or for flows near vacuum, solving the conservative Euler equations may generate negative density or internal energy numerically, which may lead to nonlinear instability and crash of the code. This difficulty is particularly profound for high order methods, for multi-material flows and for problems with moving meshes, such as the Lagrangian methods. In this paper, we construct both first order and uniformly high order accurate conservative Lagrangian schemes which preserve positivity of physically positive variables such as density and internal energy in the simulation of compressible multi-material flows with general equations of state (EOS). We first develop a positivity-preserving approximate Riemann solver for the Lagrangian scheme solving compressible Euler equations with both ideal and non-ideal EOS. Then we design a class of high order positivity-preserving and conservative Lagrangian schemes by using the essentially non-oscillatory (ENO) reconstruction, the strong stability preserving (SSP) high order time discretizations and the positivity-preserving scaling limiter which can be proven to maintain conservation and uniformly high order accuracy and is easy to implement. One-dimensional and two-dimensional numerical tests for the positivity-preserving Lagrangian schemes are provided to demonstrate the effectiveness of these methods.