Feng Xiao (Department of Mechanical Engineering, Tokyo Institute of Technology). A principle and a scheme that impact on finite volume paradigm and beyond.

In this talk, I will present two works we have recently done toward high-fidelity numerical solutions under the finite volume framework. (1) We have proposed a new principle, so-called BVD (Boundary Variation Diminishing), as a guideline to design high-resolution schemes for accurately resolving both smooth and discontinuous solutions.  We demonstrate that the BVD reconstruction is able to give numerical solutions of superior quality in comparison with existing methods. (2) We have devised a finite volume scheme, THINC (tangent of hyperbola for INterface capturing) scheme, to capture step-like solutions, including the moving interfaces in multiphase simulations. The most updated version of THINC scheme has been extended to arbitrary unstructured grids with quadratic representation of interfaces, which provides an accurate and easy-to-use interface-capturing scheme of practical significance. Implementing the THINC scheme with the BVD principle leads to substantial improvements in numerical solutions to various complex flows, which are hardly achieved by the existing methods.