Benchmark solution for unsteady state CFD problems

Abstract

Unsteady convective dominated flows are very common in engineering and science. There is a need to develop an accurate numerical scheme to predict unsteady flow and heat transfer to understand the physics of instability and the flow evolution process. No numerical scheme is free from errors. It is essential to reduce the numerical errors to some extent, so that the prediction results are dependable. This article suggests two platform problems to test the accuracy of a time marching numerical scheme. One problem is buoyancy driven flow in a differentially heated cavity. This problem has importance in melting and solidification processes. The other problem is the forced flow in an oscillatory lid driven cavity. These problems are chosen because they have well-defined geometry, boundary, and initial conditions, yet the flow exhibits complexity and skewness with the grid line High-order schemes are used to generate Benchmark solutions for the mentioned problems. It is believed that the predicted results are numerically correct and oscillation of the fluid is due to physics of the flow.