An unstructured-grid numerical model for interfacial multiphase fluids based on multi-moment finite volume formulation and THINC method. (March 2017) - Xie, Bin; Jin, Peng; Xiao, Feng
Highlights: Unstructured multi-dimensional tangent of hyperbola interface capturing (UMTHINC) scheme has been extended to hybrid arbitrary unstructured grids to capture moving interface with significantly improved solution quality. A reliable numerical model on hybrid arbitrary unstructured grids for interfacial multiphase fluid has been constructed by combining volume-average/ point-value multi-moment (VPM) method with the UMTHINC scheme. Adding the point values of velocity at the cell vertices substantially enhances the accuracy and robustness of numerical solutions. State-of-art techniques, such as the consistent formulation of mass and momentum transport for large density ratio and the pressure projection method with balanced-force model for surface tension force, are integrated to the present model to facilitate real-case application. The present model has been verified by benchmark tests, which reveals that the present numerical model provides adequate accuracy and robustness in simulating interfacial multiphase flows with complex geometry. Abstract: We present a practical numerical framework for incompressible interfacial multiphase flows on unstructured grids with arbitrary and hybrid elements. The numerical framework is constructed by combining VPM (volume-average/point-value multi-moment) and UMTHINC (unstructured multi-dimensional tangent of hyperbola interface capturing) schemes. To facilitate accurate and reliable simulations for interfacial multiphase flows on arbitrary and hybrid unstructured grids, we have made the following major new efforts in this work. (1) UMTHINC scheme on prismatic and pyramidal elements to facilitate computations on hybrid arbitrary unstructured grids; (2) Consistent numerical formulation for mass and momentum transports to simulate multiphase flows of large density ratio; (3) Combined FVM-FEM for accurate solution to diffusion equation; (4) Pressure-projection formulation in consistent with the balanced-force model. Integrating all these numerical techniques effectively enhances the accuracy and robustness in interface capturing and numerical solution of multiphase fluid dynamics, which results in a numerical framework of great significance for practical applications. Numerical verifications have been carried out through benchmark tests ranging from surface tension dominant flows of small scale to large scale flows with violently-changing interfaces. Numerical results demonstrate that the present framework is robust with adequate accuracy for simulating multiphase flows in complex geometries.