A consistent sharp interface fictitious domain method for moving boundary problems with arbitrarily polyhedral mesh

Abstract

AbstractA consistent, sharp interface fully Eulerian fictitious domain method is proposed in this article for moving boundary problems. In this method, a collocated finite volume method is used for the continuous phase; a geometry intersection method is employed for numerical integrals over the solid domain and transport of the body force; the pseudo body force defined at “solid centers” ensures the algorithm consists of the body force between the continuous form and its discretization counterpart; an explicit flux correction on cell faces and resulting mass source is introduced into the continuity equation to lower noncontinuity errors in the velocity correction step. This method is valid for stationary and moving boundary problems with arbitrarily polyhedral mesh. Several numerical tests are carried out to validate the proposed method. A second‐order spatial accuracy is found in the flow around a cylinder case, and the spurious force oscillation is well suppressed for the in‐line oscillation of a circular cylinder case. The performances on different meshes are tested, and structured mesh yields the best result, polyhedral next, and tetrahedral worst. A serial of tests is further performed on structured mesh to verify the effect of three different features (i.e., storing the body force at the solid centers, flux correction, and whether including the body force in the momentum equation) on the numerical predictions. Numerical results show that, in the in‐line oscillation of a circular cylinder, “flux correction” can eliminate the large spikes in the drag coefficient, and “including the body force in the momentum equation” helps suppress the small oscillations. For other tests, “storing the body force at the solid centers” has enormous impacts on the final results of moving boundary problems, “flux correction” has little effects and the necessity of “including the body force in the momentum equation” is case dependent.