Accurate Upwind Methods for the Euler Equations

On Consistent Time-Integration Methods for Radiation Hydrodynamics in the Equilibrium Diffusion Limit: Low-Energy-Density Regime

“…In the next section, we describe a possible technique for extending the coupled Godunov/Newton-Krylov algorithm to higher order in time for smooth regions of the fluid flow. This is done by embedding the Newton-Krylov procedure within the predictor-corrector structure of Hancock's two-step Godunov solver [33].…”

Developing High-Order Weighted Compact Nonlinear Schemes

“…Boundary and near boundary schemes are derived and asymptotic stability is analyzed on both uniform and stretching grids. For contact discontinuity sharpening, the method of Huynh [15] is adopted. In Section 3, the WCNS are applied to Euler and Navier-Stokes equations and several numerical results are obtained which show the good performances of WCNS, especially the good convergence rate and high accuracy for the boundary layer simulations.…”

A limiter for PPM that preserves accuracy at smooth extrema

“…Typically, these have been based on the idea allowing the representation of solution values outside the range defined by the cell averages [16], while still suppressing oscillations at discontinuities and underresolved gradients. In particular, the methods proposed to solve the problem to obtain uniform high-order accuracy for smooth solutions [6,8,7,13,2,10] typically have used quite elaborate analytic and / or geometric constructions. In this note, we propose a particularly simple approach to solving this problem for the PPM method [4].…”