A study of numerical methods for hyperbolic conservation laws with stiff source terms
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
Summation by parts, projections, and stability. I
Mathematics of Computation
Performance of under-resolved two-dimensional incompressible flow simulations
Journal of Computational Physics
Summation by parts, projections, and stability. II
Mathematics of Computation
Numerical simulation of shock-cylinder interactions I.: resolution
Journal of Computational Physics
SIAM Journal on Scientific Computing
Designing an efficient solution strategy for fluid flows
Journal of Computational Physics
Performance of under-resolved two-dimensional incompressible flow simulations, II
Journal of Computational Physics
Spectral Simulation of Supersonic Reactive Flows
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Low-dissipative high-order shock-capturing methods using characteristic-based filters
Journal of Computational Physics
Entropy splitting and numerical dissipation
Journal of Computational Physics
EFFICIENT IMPLEMENTATION OF WEIGHTED ENO SCHEMES
EFFICIENT IMPLEMENTATION OF WEIGHTED ENO SCHEMES
Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence
Entropy Splitting for High Order Numerical Simulation of Compressible Turbulence
High order one-step monotonicity-preserving schemes for unsteady compressible flow calculations
Journal of Computational Physics
Improvement of convective concentration fluxes in a one step reactive flow solver
Journal of Computational Physics
Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows
Journal of Computational Physics
Accurate, efficient and monotonic numerical methods for multi-dimensional compressible flows
Journal of Computational Physics
Development of low dissipative high order filter schemes for multiscale Navier-Stokes/MHD systems
Journal of Computational Physics
Multi-dimensional limiting process for three-dimensional flow physics analyses
Journal of Computational Physics
Hi-index | 31.48 |
Grid convergence of several high order methods for the computation of rapidly developing complex unsteady viscous compressible flows with a wide range of physical scales is studied. The recently developed adaptive numerical dissipation control high order methods referred to as the ACM and wavelet filter schemes are compared with a fifth-order weighted ENO (WENO) scheme. The two 2-D compressible full Navier-Stokes models considered do not possess known analytical and experimental data. Fine grid solutions from a standard second-order TVD scheme and a MUSCL scheme with limiters are used as reference solutions. The first model is a 2-D viscous analog of a shock tube problem which involves complex shock/shear/boundary-layer interactions. The second model is a supersonic reactive flow concerning fuel breakup. The fuel mixing involves circular hydrogen bubbles in air interacting with a planar moving shock wave. Both models contain fine scale structures and are stiff in the sense that even though the unsteadiness of the flows are rapidly developing, extreme grid refinement and time step restrictions are needed to resolve all the flow scales as well as the chemical reaction scales. Our computations were all made on uniform grids, and our conclusions cannot be directly carried over to, for example, curvilinear grids.