High-Order Methods for Three-Dimensional Strand-Cartesian Grids

Abstract

The flux correction method combines unstructured flux correction along body surfaces and high-order finite differences normal to surfaces. This paper builds on previous twodimensional developments of the flux correction method and extends it to three-dimensional laminar and turbulent flow on strand grids. The development of flux correction scheme applied to three-dimensions is presented. Where turbulence modeling is required, a robust version of the Spalart-Allmaras turbulence model is employed that accommodates negative values of the turbulence working variable. A unique parallel communication strategy for high-order strand grid topologies is presented which eliminates the need for "fringe" nodes or cells in each partitioned block. A semi-implicit multigrid solution algorithm is described that allows for several advantageous solution techniques to be combined for optimal efficiency in terms of memory and computation time. Fundamental verification studies are conducted, which show the flux correction method achieves high-order accuracy for both laminar and turbulent flows. A three-dimensional steady-state study of a sphere is conducted over a range of laminar Reynolds numbers. The flux correction method accurately predicts the centers and length of recirculation vortices for each Reynolds number examined, and shows excellent comparison to experimental data. The three-dimensional unsteady capabilities of flux correction are displayed through a qualitative study of vortex shedding from a sphere.

High-Order Strand Grid Methods for Multi-species Reacting Flow

“…Results shown in Figure 5 show third order and fourth order of acurracy for inviscid fluxes and viscous fluxes respectivel, and third order accuracy all fluxes and source terms. Furthermore, results match earlier works [4,6,15,16].…”

“…Note, a pseudo-time derivative is added on the left-hand side of Equation 4 to facilitate a semi-implicit time-marching solution [16]. Derivatives in the η direction are calculated via finite difference summation by parts operators.…”

“…FC is novel in that it reconstructs fluxes without the need to calculate second derivatives or higher order quadratures. The original work on FC [4,6] has been followed up with continued recent work [6,15,16] particularily in the study of higher order turbulence.…”

High-Order Strand Grid Methods for Shock Turbulence Interaction

“…Previous work on flux-correction [14,16], paved the way for more recent work [16,35,36]. The method involves correction of the flux in the unstructured plane, combined with stable summation-by-parts (SBP) operators [8,20], implemented as source terms to approximate flux derivatives along strands.…”

Sound wave in an infinite circular cylinder in the presence of viscosity and heat conductivity

“…Например, в [4] в силу отмечаемого авторами недостатка точных решений сходимость численной схемы исследу-ется на задаче типа "manufactured solution". Этот подход заключается в том, что в качестве решения берётся произвольное искусственно заданное гладкое поле, а возникающая невязка вставляется в уравнения как источник.…”