Provably Stable and High-Order Accurate Multi-Block Finite Difference Discretisation for Incompressible Flow

Abstract In this paper, we solve the velocity-pressure formulation of the incompressible Navier-Stokes equations by utilizing high-order finite difference operators that satisfy a summation-by-parts property on multi-block curvilinear domain discretizations. We apply the projection method to connect the interior multi-block interfaces, and we show the stability of the discretization through a discrete version of the energy method. Analytical test cases reveal that the discretization achieves good accuracy and high-order convergence. We also explore the efficiency of increasing the discretization order, showing that, in certain instances, a higher-order discretization provides greater accuracy while using fewer degrees of freedom. Additionally, our method reaches a good agreement with benchmark data for a well-studied benchmark problem.