Sofia Eriksson

Weak and strong wall boundary procedures and convergence to steady-state of the Navier-Stokes equations

We study the influence of different implementations of no-slip solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations. The various approaches are investigated using the energy method and an eigenvalue analysis. It is shown that the weak implementation is superior and enhances the convergence to steady-state for coarse meshes. It is also demonstrated that all the stable approaches produce the same convergence rate as the mesh size goes to zero. The numerical results obtained by using a fully nonlinear finite volume solver support the theoretical findings from the linear analysis.

The influence of weak and strong solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations

The influence of weak and strong solid wall boundary conditions on the convergence to steady-state of the Navier-Stokes equations

A stable and conservative method for locally adapting the design order of finite difference schemes

A stable and conservative method for locally adapting the design order of finite difference schemes

A Dual Consistent Finite Difference Method with Narrow Stencil Second Derivative Operators

We study the numerical solutions of time-dependent systems of partial differential equations, focusing on the implementation of boundary conditions. The numerical method considered is a finite difference scheme constructed by high order summation by parts operators, combined with a boundary procedure using penalties (SBP–SAT). Recently it was shown that SBP–SAT finite difference methods can yield superconvergent functional output if the boundary conditions are imposed such that the discretization is dual consistent. We generalize these results so that they include a broader range of boundary conditions and penalty parameters. The results are also generalized to hold for narrow-stencil second derivative operators. The derivations are supported by numerical experiments.

Exact Non-reflecting Boundary Conditions Revisited: Well-Posedness and Stability

Exact non-reflecting boundary conditions for a linear incompletely parabolic system in one dimension have been studied. The system is a model for the linearized compressible Navier–Stokes equations, but is less complicated which allows for a detailed analysis without approximations. It is shown that well-posedness is a fundamental property of the exact non-reflecting boundary conditions. By using summation by parts operators for the numerical approximation and a weak boundary implementation, it is also shown that energy stability follows automatically.

Analysis of mesh and boundary effects on the accuracy of node-centered finite volume schemes

Analysis of mesh and boundary effects on the accuracy of node-centered finite volume schemes

Well-posedness and stability of exact non-reflecting boundary conditions

Exact non-reflecting boundary conditions for an incompletely parabolic system have been studied. It is shown that well-posedness is a fundamental property of the non-reflecting boundary conditions. ...