High-Order Linear and Non-Linear Residual Distribution Schemes for the Simulation of Compressible Viscous Flows

Speaker: Dante De Santis, Department of Aeronautics & Astronautics, Stanford University
March 26, 2015

Presentation

Abstract

Residual Distribution (RD) schemes represent an interesting alternative to Discontinuous Galerkin (DG) schemes. While computationally compact and probably more flexible, DG schemes suffer from the serious drawback of a very fast growth of the number of degrees of freedom with the cell polynomial degree. In RD schemes the formulation remains local, as in DG, but the number of degrees of freedom grows less quickly. The price to pay is to impose a continuous approximation of the solution. An additional advantage of RD methods is the possibility to construct non-linear schemes which are at the same time high-order accurate and monotone across the shocks, without the necessity to introduce artificial viscosity or complex reconstruction of the solution. In this presentation implicit high-order Residual Distribution schemes for the solution of the compressible Navier Stokes and RANS equations are described. The accuracy of the numerical scheme is investigated and finally the method is used to perform the simulation of several 2D/3D problems.

Biography

De Santis is a postdoctoral fellow in the Department of Aeronautics & Astronautics at Stanford University. He holds a BSc. degree and a MSc. degree in Aeronautical Engineering from Politecnico di Milano. In 2013, he received his Ph.D. in Applied Mathematics and Informatics from University of Bordeaux. His research interests are high-order method in computational fluid dynamics, immersed boundary methods for fluid-structure interaction problem and gradient-based shape optimization.

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