Energy-Conserving Navier-Stokes Solver. Verification of steady laminar flows

This report describes the verification of a second order ‘energy-conserving’ finite volume method, for the solution of the incompressible Navier-Stokes equations on staggered, cartesian grids. Four different test cases are examined, being channel flow, lid-driven cavity flow, backward-facing step flow and flow through an actuator disk. The accuracy of the spatial discretization is investigated by looking at laminar, steady flow. Second order accuracy is shown for velocity and pressure on uniform and non-uniform meshes, in 2D and 3D, and for different boundary conditions. In the case of flow through an actuator disk a discontinuity in the pressure is present, which is correctly captured by the method. The method is suitable to be extended to compute unsteady turbulent flows, such as the flow of air in wind turbine wakes.

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