Abstract
We present a high-order meshless method based on scattered data interpolation for solving Multiphysics problems in complex domains. A complex domain is first represented by scattered points generated by any method, including as vertices of a finite element grid. The flow variables are located at the scattered points and interpolated over a local cloud of points using a radial basis function (RBF). We consider Polyharmonic splines (PHS) which do not need a shape parameter. We further append a polynomial of desired degree to achieve high order discretization accuracy. To solve the Navier-Stokes equations, the partial-derivatives are evaluated by differentiating the radial basis functions and the polynomials. We have developed an explicit fractional step method and a semi-implicit method to integrate the Navier-Stokes and energy equations in time with high spatial and second-order temporal accuracies. The explicit fractional step method is limited by the combined convective and diffusive Courant numbers while the semi-implicit method can use time steps 10-20 times the explicit time step. A three-dimensional extension for periodic problems has been developed with Fourier expansions in the periodic direction. We demonstrate the method has high spatial discretization accuracy.
About the Speaker
Pratap Vanka is Professor Emeritus in the Department of Mechanical Science and Engineering, UIUC. He and his students have developed several numerical algorithms for fluid flows including multigrid based flow solvers, Lattice Boltzmann methods, meshless techniques, GPU based methods, and partially-parabolic methods. He has taught a graduate level CFD course in the department for more than 30 years. He worked for his Ph. D. with Professor D. B. Spalding, a pioneer in computational fluid dynamics and computational heat transfer. Pratap Vanka has published papers on heat transfer, metal solidification, combustion, and computational methods. He is a Life Fellow of ASME, Fellow of APS, Associate Fellow of AIAA, and recipient of the ASME Freeman Scholar lecture award and other research awards.
Host: Professor Leonardo Chamorro
