Aerodynamic design via control theory
Journal of Scientific Computing
Journal of Computational Physics
Summation by parts for finite difference approximations for d/dx
Journal of Computational Physics
A stable and conservative interface treatment of arbitrary spatial accuracy
Journal of Computational Physics
Journal of Computational Physics
Journal of Scientific Computing
High-order finite difference methods, multidimensional linear problems, and curvilinear coordinates
Journal of Computational Physics
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows
Journal of Computational Physics
On Coordinate Transformations for Summation-by-Parts Operators
Journal of Scientific Computing
Adjoint and defect error bounding and correction for functional estimates
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
Journal of Scientific Computing
On the order of accuracy for difference approximations of initial-boundary value problems
Journal of Computational Physics
Journal of Computational Physics
Error Bounded Schemes for Time-dependent Hyperbolic Problems
SIAM Journal on Scientific Computing
Superconvergent Functional Estimates from Summation-By-Parts Finite-Difference Discretizations
SIAM Journal on Scientific Computing
Journal of Computational Physics
Journal of Scientific Computing
Journal of Computational Physics
Applied Numerical Mathematics
Summation-by-parts operators and high-order quadrature
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Journal of Computational Physics
Hi-index | 31.46 |
In this paper we derive well-posed boundary conditions for a linear incompletely parabolic system of equations, which can be viewed as a model problem for the compressible Navier-Stokes equations. We show a general procedure for the construction of the boundary conditions such that both the primal and dual equations are well-posed. The form of the boundary conditions is chosen such that reduction to first order form with its complications can be avoided. The primal equation is discretized using finite difference operators on summation-by-parts form with weak boundary conditions. It is shown that the discretization can be made energy stable, and that energy stability is sufficient for dual consistency. Since reduction to first order form can be avoided, the discretization is significantly simpler compared to a discretization using Dirichlet boundary conditions. We compare the new boundary conditions with standard Dirichlet boundary conditions in terms of rate of convergence, errors and discrete spectra. It is shown that the scheme with the new boundary conditions is not only far simpler, but also has smaller errors, error bounded properties, and highly optimizable eigenvalues, while maintaining all desirable properties of a dual consistent discretization.