Multi-block High-order Finite Difference Method for the Incompressible Navier-Stokes Equations in Complex Geometry

  • Niemelä, David (Uppsala University)

Please login to view abstract download link

We solve the incompressible Navier-Stokes equations in complex geometry using a multi-block high-order finite difference scheme with summation-by-parts (SBP) properties. The work is a continuation of the work in \cite{Gustavs}, with the continuation of curvilinear multi-block geometries. Making use of the Projection method \cite{Projection} for interface and boundary implementations the boundary conditions are imposed strongly, as separate from the usual \textit{Simultaneous-Approximation-Terms} (SAT) boundary method commonly seen in SBP-schemes. Something shown in \cite{Gustavs} to improve the accuracy of near boundary effects, such as vortices. Using SBP operators the well-posedness analysis of the discrete scheme can be directly related via the Energy method to the continuous well-posedness analysis, showing energy conservation of the system. Stability for the scheme is proven using the Energy method for the curvilinearly transformed equations and convergence of expected order is shown for the analytic Taylor-Green vortex problem on complex coupled multi-block geometries. Classical benchmark problems as the cylinder in a flow is also solved.