Computer Methods in Applied Mechanics and Engineering
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
A Stable Penalty Method for the Compressible Navier--Stokes Equations: I. Open Boundary Conditions
SIAM Journal on Scientific Computing
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Computational Physics
High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
Journal of Computational Physics
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
Stable and Accurate Artificial Dissipation
Journal of Scientific Computing
Summation by parts operators for finite difference approximations of second derivatives
Journal of Computational Physics
Steady-State Computations Using Summation-by-Parts Operators
Journal of Scientific Computing
Well-Posed Boundary Conditions for the Navier--Stokes Equations
SIAM Journal on Numerical Analysis
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
Journal of Computational Physics
Stable and accurate schemes for the compressible Navier-Stokes equations
Journal of Computational Physics
A stable and conservative high order multi-block method for the compressible Navier-Stokes equations
Journal of Computational Physics
A stable and high-order accurate conjugate heat transfer problem
Journal of Computational Physics
Revisiting and Extending Interface Penalties for Multi-domain Summation-by-Parts Operators
Journal of Scientific Computing
Stable and Accurate Interpolation Operators for High-Order Multiblock Finite Difference Methods
SIAM Journal on Scientific Computing
Stable Robin solid wall boundary conditions for the Navier-Stokes equations
Journal of Computational Physics
Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
SIAM Journal on Scientific Computing
Verification of variable-density flow solvers using manufactured solutions
Journal of Computational Physics
Output error estimation for summation-by-parts finite-difference schemes
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Summation-by-parts operators and high-order quadrature
Journal of Computational and Applied Mathematics
On the impact of boundary conditions on dual consistent finite difference discretizations
Journal of Computational Physics
Journal of Scientific Computing
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In this paper we derive new far-field boundary conditions for the time-dependent Navier-Stokes and Euler equations in two space dimensions. The new boundary conditions are derived by simultaneously considering well-posedness of both the primal and dual problems. We moreover require that the boundary conditions for the primal and dual Navier-Stokes equations converge to well-posed boundary conditions for the primal and dual Euler equations. We perform computations with a high-order finite difference scheme on summation-by-parts form with the new boundary conditions imposed weakly by the simultaneous approximation term. We prove that the scheme is both energy stable and dual consistent and show numerically that both linear and non-linear integral functionals become superconvergent.