An Unstructured Grid Incompressible Navier-Stokes Algorithm for Convective Heat Transfer Based on Artificial Compressibility
A Thesis Presented for the Master of Science in Computational Engineering Degree, The University of Tennessee at Chattanooga
Jessica Elaine Kress, December 2012
The development of an explicit unstructured grid finite-volume scheme for solving the full incompressible Navier-Stokes equations along with the energy equation in a strongly coupled manner is presented. The Boussinesq approximation is utilized to account for thermal buoyancy. The method of artificial compressibility is used to solve the resulting equations in a time marching fashion. Roe’s approximate Riemann solver is used for the construction of the numerical flux. An eigensystem is derived for the flux Jacobian matrix, which is used in the evaluation of the numerical flux and the characteristic variable boundary conditions. The resulting algorithm is validated by simulating canonical test cases from the three regimes of convective heat transfer. The computed solutions are in close agreement with analytical solutions and other benchmark computations.
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