March 14, 2014
Speaker: Clinton Groth (CFD and Propulsion group, UTIAS, University of Toronto)
Title: Parallel High-Order Adaptive Mesh Refinement Finite-Volume Schemes for Multi-Scale Physically-Complex Flows
Abstract: A family of high-order central essentially non-oscillatory (CENO) finite-volume schemes with adaptive mesh refinement (AMR) are described for the prediction of a range of multi-scale physically-complex flows in both two and three space dimensions. The CENO schemes are based on a hybrid solution reconstruction procedure that combines an unlimited high-order k-exact, least-squares reconstruction technique, following from a fixed central stencil, with a monotonicity preserving limited piecewise linear least-squares reconstruction. Switching in the hybrid procedure is determined by a solution smoothness indicator that detects whether or not the solution is accurately represented on the mesh. The solution smoothness indicator is also used in the formulation of a refinement criteria for directing mesh adaptation. The proposed approach avoids some of the complexities associated with the original essentially non-oscillatory (ENO) and other weighted ENO (WENO) schemes and is well-suited for solution reconstruction on irregular and unstructured mesh. The development of the high-order finite-volume with AMR approach for both multi-block body-fitted and more generally unstructured meshes in both two- and three-dimensions is discussed for a range of applications, including inviscid compressible flows, perfectly conducting plasma flows, viscous incompressible and compressible flows, as well as reactive flows. The ability of the CENO schemes to accurately represent solutions with smooth extrema and yet robustly handle under-resolved and/or non-smooth solution content is demonstrated.