PDE/Applied Math Seminar

Event Date: 

Friday, November 4, 2016 - 3:00pm to 4:00pm
Title: Towards Fourth- and Higher-order Numerical Simulations of Incompressible Flows with Moving Boundaries


Speaker: Qinghai Zhang School of Mathematical Sciences, Zhejiang University
Abstract: A generic projection maps one vector to another such that their difference is a gradient field and the projected vector does not have to be solenoidal. Via a commutator of Laplacian and the generic projection, I reformulate the incompressible Navier-Stokes equations as the sole evolution of a projected velocity, with the incompressibility constraint enforced by a pressure Poisson equation so that the dissipation of velocity divergence is governed by a heat equation. As a prominent advantage of this formulation, it is trivial to adopt another time integrator for an even higher order of accuracy. This finite-volume solver is further augmented with parallel computing and adaptive mesh refinement. Irregular and moving phases are modeled by semi-analytic regular open sets. Based on Boolean operations of these sets and the author's work on donating regions, we propose MARS, a systematic framework for analyzing explicit interface tracking methods including volume-of- fluid methods, front tracking methods, and the recent iPAM method. Under MARS, several dicult interface-tracking tests are resolved to machine precision. Furthermore, interface curvature can be efficiently estimated to the best attainable accuracy admitted by double-precision floating point numbers.