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Center for Nonlinear Studies |
The numerical simulation of incompressible multiphase flow can be beneficial in predicting flows around a swimming whale, atomization of fuel in an internal combustion engine, and flows in microfluidic devices. We have made two new developments which significantly accelerate the simulation of these flows: (1) We have developed a hybrid level set and volume constraint method (LSVC) for representing dynamic, complex, interfaces with zero volume fluctuation, and (2) we have extended the multigrid preconditioned conjugate gradient method (MGPCG) so that one can solve elliptic equations with singular source terms and discontinuous coefficients on a hierarchy of grids (block structured adaptive mesh refinement) with a guarantee for convergence. The LSVC method enables one to easily simulate multiphase problems on unstructured meshes, or on meshes in which a gas/liquid interface is not wholly contained on the finest adaptive level. Also, for multiphase problems with an embedded solid undergoing solid-body motion or perhaps an embedded deforming solid, it is trivial to conserve liquid/gas volume with the LSVC method without complicated refluxing procedures in cut cells containing liquid,solid, and gas. The new MGPCG method for adaptive grids has the same advantages over MG (multigrid) or ICPCG (incomplete Cholesky preconditioned conjugate gradient method) that the original MGPCG method (developed by Tatebe) had on a single grid. We prove that the new adaptive MGPCG method is guaranteed to converge regardless of the coefficients or source terms. We show by example that the adaptive MGPCG method is 3 times faster than PCG or MG on adaptive grids. The adaptive MGPCG method becomes especially more efficient as one increases the number of levels of adaptivity, or if the air/water interface is not wholly contained on the finest adaptive level. The new adaptive MGPCG solver is so fast, that the pressure projection step is no longer the step that consumes the most CPU time insolving the Navier-Stokes equations for inncompressible multi-phase flow.
Host: Mikhail Shashkov. shashkov@lanl.gov, 667-4400