A consistent method for finite volume discretization of body forces on collocated grids applied to flow through an actuator disk

• We present a consistent method for discretizing body forces for incompressible CFD.
• The method eliminates numerical wiggles created near discontinuous body forces.
• The method is independent of a free smearing parameter.
• The method provides a sharp representation of actuator surfaces in collocated grids.

This paper describes a consistent algorithm for eliminating the numerical wiggles appearing when solving the finite volume discretized Navier–Stokes equations with discrete body forces in a collocated grid arrangement. The proposed method is a modification of the Rhie–Chow algorithm where the force in a cell is spread on neighboring cells by applying equivalent pressure jumps at the cell faces. The method shows excellent results when applied for simulating the flow through an actuator disk, which is relevant for wind turbine wake simulations.