Abstract
Vorticity-stream function method and MAC algorithm are adopted to systemically compare the finite volume method (FVM) and finite difference method (FDM) in this paper. Two typical problems—lid-driven flow and natural convection flow in a square cavity—are taken as examples to compare and analyze the calculation performances of FVM and FDM with variant mesh densities, discrete forms, and treatments of boundary condition. It is indicated that FVM is superior to FDM from the perspective of accuracy, stability of convection term, robustness, and calculation efficiency. Particularly ,when the mesh is coarse and taken as20×20, the results of FDM suffer severe oscillation and even lose physical meaning.
Highlights
In the numerical solution of flow and heat transfer problems, the concepts of conservative and nonconservative equations were firstly proposed in [1, 2] in the 1980s
The accuracy of finite volume method (FVM) and finite difference method (FDM) is evaluated by comparing bench mark solution with the results
(1) No matter which algorithm, discrete form, or treatment of boundary condition is adopted, the results obtained by conservative FVM are closer to benchmark solution than those obtained by FDM
Summary
In the numerical solution of flow and heat transfer problems, the concepts of conservative and nonconservative equations were firstly proposed in [1, 2] in the 1980s. The numerical calculation is implemented on the calculation unit of finite size, for which the two forms of equations are of different characteristics. Practical calculation process shows that the influence of differences between conservative and nonconservative forms on accuracy, stability, and efficiency of numerical calculation is significant. Conservative governing equation and the corresponding discrete form show some advantages; for example, in the control volume with finite size, only the conservative equation can guarantee that the conservation law of the problem studied is satisfied [3,4,5]. In the calculation of flow problem involving shock wave, the obtained flow field is usually smooth and stable employing the conservation form of governing equation, while using the non-conservation equation might lead to unsatisfactory spatial oscillations in the upstream and downstream regions of the shock wave [6,7,8]. The present paper compares the calculation performances by analyzing the finite volume method which is conservative and finite difference method which is nonconservative
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