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Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations
Time-stable boundary conditions for finite-difference schemes solving hyperbolic systems: methodology and application to high-order compact schemes
Abstract We present a systematic method for constructing boundary conditions (numerical and physical) of the required accuracy, for compact (Pade-like) high-order finite-difference schemes for…
Fourth-order 2N-storage Runge-Kutta schemes
A family of five-stage fourth-order Runge-Kutta schemes is derived; these schemes required only two storage locations and are considerably more efficient and accurate than existing third-order low-storage schemes.
Low-storage, Explicit Runge-Kutta Schemes for the Compressible Navier-Stokes Equations
A Stable and Conservative Interface Treatment of Arbitrary Spatial Accuracy
Stable and accurate interface conditions based on the SAT penalty method are derived for the linear advection?diffusion equation. The conditions are functionally independent of the spatial order of…
Entropy Stable Spectral Collocation Schemes for the Navier-Stokes Equations: Discontinuous Interfaces
Nonlinear entropy stability and a summation-by-parts framework are used to derive provably stable, polynomial-based spectral collocation element methods of arbitrary order for the compressible…
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
Block-to-block interface interpolation operators are constructed for several common high-order finite difference discretizations that maintain the strict stability, accuracy, and conservation properties of the base scheme even when nonconforming grids or dissimilar operators are used in adjoining blocks.
The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes
The stability characteristics of various compact fourth- and sixth-order spatial operators are assessed with the theory of Gustafsson, Kreiss, and Sundstrom (G-K-S) for the semidiscrete initial…
High-order entropy stable finite difference schemes for nonlinear conservation laws: Finite domains
Implicit Time Integration Schemes for the Unsteady Compressible Navier–Stokes Equations: Laminar Flow
It is concluded that reliable integration is most efficiently provided by fourth-order Runge–Kutta methods for this problem where order reduction is not observed.