Review of summation-by-parts operators with simultaneous approximation terms for the numerical solution of partial differential equations
Abstract Summation-by-parts (SBP) operators have a number of properties that make them
an attractive option for higher-order spatial discretizations of partial differential equations. In …
an attractive option for higher-order spatial discretizations of partial differential equations. In …
[HTML][HTML] Continuum and discrete initial-boundary value problems and Einstein's field equations
Many evolution problems in physics are described by partial differential equations on an
infinite domain; therefore, one is interested in the solutions to such problems for a given …
infinite domain; therefore, one is interested in the solutions to such problems for a given …
Review of summation-by-parts schemes for initial–boundary-value problems
High-order finite difference methods are efficient, easy to program, scale well in multiple
dimensions and can be modified locally for various reasons (such as shock treatment for …
dimensions and can be modified locally for various reasons (such as shock treatment for …
A volume-filtered description of compressible particle-laden flows
In this work, we present a rigorous derivation of the volume-filtered viscous compressible
Navier–Stokes equations for disperse two-phase flows. Compared to incompressible flows …
Navier–Stokes equations for disperse two-phase flows. Compared to incompressible flows …
A generalized framework for nodal first derivative summation-by-parts operators
A generalized framework is presented that extends the classical theory of finite-difference
summation-by-parts (SBP) operators to include a wide range of operators, where the main …
summation-by-parts (SBP) operators to include a wide range of operators, where the main …
A stable high-order finite difference scheme for the compressible Navier–Stokes equations, far-field boundary conditions
We construct a stable high-order finite difference scheme for the compressible Navier–
Stokes equations, that satisfy an energy estimate. The equations are discretized with high …
Stokes equations, that satisfy an energy estimate. The equations are discretized with high …
Summation by parts operators for finite difference approximations of second-derivatives with variable coefficients
K Mattsson - Journal of Scientific Computing, 2012 - Springer
Finite difference operators approximating second derivatives with variable coefficients and
satisfying a summation-by-parts rule have been derived for the second-, fourth-and sixth …
satisfying a summation-by-parts rule have been derived for the second-, fourth-and sixth …
Multidimensional summation-by-parts operators: general theory and application to simplex elements
Summation-by-parts (SBP) finite-difference discretizations share many attractive properties
with Galerkin finite-element methods (FEMs), including time stability and superconvergent …
with Galerkin finite-element methods (FEMs), including time stability and superconvergent …
On the order of accuracy for difference approximations of initial-boundary value problems
Finite difference approximations of the second derivative in space appearing in, parabolic,
incompletely parabolic systems of, and 2nd-order hyperbolic, partial differential equations …
incompletely parabolic systems of, and 2nd-order hyperbolic, partial differential equations …
A stable high-order finite difference scheme for the compressible Navier–Stokes equations: no-slip wall boundary conditions
A stable wall boundary procedure is derived for the discretized compressible Navier–Stokes
equations. The procedure leads to an energy estimate for the linearized equations. We …
equations. The procedure leads to an energy estimate for the linearized equations. We …