High-Order Schemes for Compressible Viscous Flows

SHYAM SUNDAR DHANABALAN

Publication

High-Order Schemes for Compressible Viscous Flows

SHYAM SUNDAR DHANABALAN

Abstract

This thesis presents development of a set of high order, high resolution numerical methods for efficient solution of inviscid and viscous compressible flows. Numerical methods are developed by considering finite information propagation within the elements over a give time integration step. Spatial discretization schemes of up to fifth order accuracy have been developed and successfully tested for unstructured grids. The concept is also extended for computing the solution gradients at the element interface. The experience gained while designing the numerical methods was applied for development of high resolution WENO shock capturing schemes and adaptive time stepping techniques. Numerical experiments demonstrate that the proposed schemes can reproduce higher order characteristics in all the cases while retaining the advantages of efficiency of computation and simplicity in implementation. The entire set of numerical methods developed in this work are tested on viscous compressible flow problems involving aero-acoustic sound generation.