Implicit TVD Schemes for Hyperbolic Conservation Laws in Curvilinear Coordinates
A one-parameter family of explicit and implicit upwind second-order-accurate, total variation diminishing (TVD) schemes has been developed by Harten. These TVD schemes have the property of not...
View ArticleSemi-Implicit and Fully Implicit Shock-Capturing Methods for Nonequilibrium...
Some numerical aspects of finite-difference algorithms for nonlinear multidimensional hyperbolic conservation laws with stiff nonhomogeneous (source) terms are discussed. If the stiffness is entirely...
View ArticleBoundary Approximations for Implicit Schemes for .One-Dimensional Inviscid...
The applicability to practical calculations of recent theoretical developments in the stability analysis of difference approximations is examined for initial boundary-value problems of the hyperbolic...
View ArticleSkew-symmetric splitting of high-order central schemes with nonlinear filters...
A class of high-order nonlinear filter schemes by Yee et al. (J Comput Phys 150:199–238, 1999), Sjögreen and Yee (J Comput Phys 225:910–934, 2007), and Kotov et al. (Commun Comput Phys 19:273–300,...
View ArticleHigh-order finite-difference nonlinear filter methods for subsonic turbulence...
Numerical stability of high-order fi lter schemes developed by Yee & Sjogreen is tested on thr~dimensional turbulence simulations with stochastic forcing and their performance is compared with...
View ArticleA Class of High-Resolution Explicit and Implicit Shock-Capturing Methods
The development of shock-capturing finite difference methods for hyperbolic conservation laws has been a rapidly growing area for the last decade. Many of the fundamental concepts, state-of-the-art...
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.
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 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 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 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 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 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 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 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 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 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 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 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 ArticleTwo 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...
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