Two Decades Old Entropy Stable Method for the Euler Equations Revisited
The two decades old high order central differencing via entropy splitting and summation-by-parts (SBP) difference closure of Olsson and Oliger, Gerritsen and Olsson, and Yee et al. [2, 7, 25] is...
View ArticleOn Skew-Symmetric Splitting and Entropy Conservation Schemes for the Euler...
The Tadmor type of entropy conservation formulation for the Euler equations and various skew-symmetric splittings of the inviscid flux derivatives are discussed. Numerical stability of high order...
View ArticleUpwind and Symmetric Shock- Capturing Schemes
The development of numerical methods for hyperbolic conservation laws has been a rapidly growing area for the last ten years. Many of the fundamental concepts and state-of-the-art developments can...
View ArticleImplicit Total Variation Diminishing (TVD) Schemes for Steady-State Calculations
We examine the application of a new implicit unconditionally-stable high-resolution TVD scheme to steady-state calculations. It is a member of a one-parameter family of explicit and implicit...
View ArticleEntropy Splitting for High Order Numerical Simulation of Vortex Sound at Low...
Several recent developments in efficient, stable, highly parallelizable high order non-dissipative spatial schemes with characteristic based filters that exhibit low dissipation for long time linear...
View ArticleNonlinear filtering in compact high-order schemes
The adaptive nonlinear filtering approach for shock/turbulence gas dynamics and magnetohydrodynamics (MHD) flows adopted in our previous work is employed in conjunction with compact high-order methods...
View ArticleOn Entropy Conservation and Kinetic Energy Preservation Methods
The Tadmor-type entropy conservative method using the mathematical logarithmic entropy function and two forms of the Sjögreen & Yee entropy conservative methods using the Harten entropy function...
View ArticleComparative study of high order methods for subsonic turbulence simulation...
A class of spatially seventh-order nonlinear filter methods with adaptive dissipation control developed by Yee & Sjögreen [1, 2] is tested on three-dimensional subsonic turbulence simulations with...
View ArticleHigh order entropy conservative central schemes for wide ranges of...
The Sjogreen and Yee [31]high order entropy conservative numerical method for compressible gas dynamics is extended to include discontinuities and also extended to equations of ideal...
View ArticleCorrigendum to “On High Order Finite-Difference Metric Discretizations...
The authors regret that the already published version contains some typographic errors in the formulas for the Runge-Kutta moving metric time stepping method.
View ArticleSpurious behavior of shock-capturing methods by the fractional step approach:...
The goal of this paper is to relate numerical dissipations that are inherited in high order shock-capturing schemes with the onset of wrong propagation speed of discontinuities. For pointwise...
View ArticleHigh order finite difference methods with subcell resolution for advection...
A new high order finite-difference method utilizing the idea of Harten ENO subcell resolution method is proposed for chemical reactive flows and combustion. In reaction problems, when the reaction...
View ArticleHigh Order Well-Balanced Schemes and Applications to Non-Equilibrium Flow...
The stiffness of the source terms in modeling non-equilibrium ow problems containing finite-rate chemistry or combustion poses additional numerical difficulties beyond that for solving non-reacting...
View ArticleEntropy Splitting for High Order Numerical Simulation of Vortex Sound at Low...
A method of minimizing numerical errors, and improving nonlinear stability and accuracy associated with low Mach number computational aeroacoustics (CAA) is proposed. The method consists of two levels.
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