Accuracy evaluation of unsteady CFD numerical schemes by vortex preservation

• Published in: Computers & fluids Vol. 24; no. 8; pp. 883 - 895
• Main Authors: Davoudzadeh, F., McDonald, H., Thompson, B.E.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 1995; Elsevier Science
• Subjects: Calculations; Computational methods in fluid dynamics; Diffusion; Errors; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Heat convection; Iterative methods; Navier Stokes equations; Numerical methods; Physics; Unsteady flow; Vortex flow; Fluid mechanics; Error estimation; Computational fluid dynamics; Vorticity; Vortex motion; Numerical method; Unsteady flow; Iterative methods; Navier-Stokes equations
• ISSN: 0045-7930; 1879-0747
• DOI: 10.1016/0045-7930(95)00023-6

Numerical uncertainty is an important but sensitive subject in computational fluid dynamics and there is a need for improved methods to quantify calculation accuracy. A known analytical solution, a Lamb-type vortex unsteady movement in a free stream, is compared to the numerical solutions obtained from different numerical schemes to assess their temporal accuracies. Solving the Navier-Stokes equations and using the standard Linearized Block Implicit ADI scheme, with first order accuracy in time second order in space, a vortex is convected and results show the rapid diffusion of the vortex. These calculations were repeated with the iterative implicit ADI scheme which has second-order time accuracy. A considerable improvement was noticed. The results of a similar calculation using an iterative fifth-order spatial upwind-biased scheme is also considered. The findings of the present paper demonstrate the needs and provide a means for quantification of both distribution and absolute values of numerical error.