Unstructured, Pressure-Based Algorithm Using Implicit Runge–Kutta for Moving Boundary Problems

Abstract

An unstructured, pressure-based algorithm, IRK-SIMPLER, is developed for simulating two-dimensional incompressible flows over moving bodies. The Navier–Stokes equations in the arbitrary Lagrangian Eulerian form are discretized using collocated, median-dual control volumes with a flux correction method. The semidiscrete form is integrated in time using a diagonally implicit Runge–Kutta method. The unstructured discretization of the spatial computational domain is composed of a circular body-fitted grid, a rectangular patch grid, and a background grid. The motion of the bodies is decomposed into a series of rotations and translations. Rotation is achieved by rotating the body-fitted grid along with the body and flipping the edges of the appropriate cells. Translation is achieved by morphing the patch grid as the body moves. For large translational displacements, the rectangular patch grid is moved with the body and rematched with the background grid to obtain a new conforming grid. The algorithm is validated for multiple incompressible flow cases.