On spurious behavior of CFD simulations

Abstract

Spurious behavior in underresolved grids and/or semi-implicit temporal discretizations for four computational fluid dynamics (CFD) simulations are studied. The numerical simulations consist of (a) a 1-D chemically relaxed nonequilibrium model, (b) the direct numerical simulation (DNS) of 2-D incompressible flow over a backward facing step, (c) a loosely-coupled approach for a 2-D fluid-structure interaction, and (d) a 3-D compressible unsteady flow simulation of vortex breakdown in delta wings. Using knowledge from dynamical systems theory, various types of spurious behaviors that are numerical artifacts were systematically identified. These studies revealed the various possible dangers of misinterpreting numerical simulation of realistic complex flows that are constrained by the available computing power. In large scale computations underresolved grids, semi-implicit procedures, loosely-coupled implicit procedures, and insufficiently long time integration in DNS are most often unavoidable. Consequently, care must be taken in both computation and in interpretation of the numerical data. The results presented confirm the important role that dynamical systems theory can play in the understanding of the nonlinear behavior of numerical algorithms and in aiding the identification of the sources of numerical uncertainties in CFD.

Towards steady-state solutions for supersonic wind accretion on to gravitating objects

“…As noted by Yee & Sweby (1998), a straightforward application of well‐validated codes for the simulation of insufficiently understood physical problems can result in wrong results, excessively slow convergence, or even non‐convergent solutions. Various results (Yee et al 1999) show the importance of the theory of dynamical systems in understanding the non‐linear behaviour of numerical algorithms and in revealing the sources of numerical uncertainties. Application of the specific dynamical systems theory technique to the wind accretion problem is the subject of the future work.…”

Meshless solution of laminar flow in a 2D backward-facing step

“…Here the bilinear interpolation produces nonphysical oscillations and some nonlinear interpolation schemes have been proposed with great success, as for example [24]. On the other hand, the segregated approach, where velocity components and pressure are located at different positions and interpolation for the convection terms is needed.…”

“…Re-attachment increases always. One stability analysis through 2D DNS simulations can be seen in [24], where calculations are done for Reynolds number of 500 and 800 with different grid sizes. A very interesting study can be found in [25], where a streamline-vorticity formulation is used.…”

Flow structure in a short chamber of a labyrinth seal with a backward-facing step

“…However, other elements such as discretization, iteration step sizes, and solver methodology can equally affect the numerical results. Over the past decades, extensive studies have been published on the analysis of numerical uncertainties related to CFD [33], e.g., time-marching approaches [32], discretization of advective terms [9], slow-developing solutions due to machine round-off [30]. Recent works on this topic cover various types of flows spreading from multiple steady-state RANS solutions for airfoil aerodynamics problems [18] to spurious behavior of systems with stiff source terms and discontinuities [20].…”