Spatial accuracy and performance of a mixed‐order, explicit multi‐stage method for unsteady flows

Abstract

SUMMARYWe assess the spatial accuracy and performance of a mixed‐order, explicit multi‐stage method in which an inexpensive low‐order scheme is used for the initial stages, and a more expensive high‐order scheme is used for the final stage only. Compared with the use of a high‐order scheme for all stages, we observe that the mixed‐order scheme achieves comparable accuracy and convergence while providing a speed‐up of a factor of two on mesh sizes of O(106 − 107) tetrahedron. For calculations with significant adaptive mesh refinement, a more modest speed‐up of 30% is obtained. Published 2012. This article is a US Government work and is in the public domain in the USA.

Performance of a three‐dimensional unstructured mesh compressible flow solver on NVIDIA Fermi‐class graphics processing unit hardware

“…Within the four‐stage time integration scheme, edge‐centered fluxes are calculated with a simple Roe‐type method for k < n , and with a higher‐order MUSCL reconstruction for k = n . The use of low‐order methods during the initial Runge–Kutta stages has been found to give a notable reduction in computational time without compromising overall accuracy . This approach does, however, lower the overall compute intensity of the scheme and hence the potential performance improvement that can be achieved with GPU hardware.…”