Abstract
Problem statement: Pressure and velocity decoupling have been source of problem in solving Navier-Stokes and continuity equation particularly in complex collocated grid. The problem of pressure velocity decoupling is usually reduced by using momentum interpolation to calculate mass flux at face of control volume. Equation of momentum interpolation was derived by assumption that the face of cell is equidistant from two neighbor cell centers and face of cell is collinear with two neighbor cell centers. This assumption is not valid in many unstructured grid and cause significant error. Approach: In this article a simple improvement of momentum interpolation for using in unstructured grid was proposed. The improvement was done by added a correction term to original equation. Results: The method was compared with original method in Kovasznay’s flow and Laminar Poisseulli Flow. The method was found able to reduce error about 40% in both cases. Conclusion: The correction added to original momentum interpolation is able to reduce error in Navier-Stokes equation solver on unstructured grid.
Highlights
Only very limited number of study related to accuracy of application of the Rhie and Chow (1983)
Mathur and Murthy (1997) applied momentum interpolation to unstructured grid by assuming the face is laid down inline and in the middle between two neighbor cell centers where the interpolation was claimed formally second order
Accuracy of both momentum interpolation in calculate laminar Poisseulli flow is shown through contour of velocity and velocity distribution along centre line of flow channel as shown in Fig. 6 and 7 respectively
Summary
Only very limited number of study related to accuracy of application of the Rhie and Chow (1983). The momentum interpolation of Rhie and Chow (1983) is popularly used to calculate face velocity in discretised momentum equation for SIMPLE based algorithm since. A popularly used method to implement Rhie and Chow (1983) interpolation method on unstructured grid is based on the way proposed by Mathur and Murthy (1997). Mathur and Murthy (1997) applied momentum interpolation to unstructured grid by assuming the face is laid down inline and in the middle between two neighbor cell centers where the interpolation was claimed formally second order. In this study a simple modification to interpolation of Mathur and Murthy (1997) in order to solve this problem is proposed. Kovasznay’s flow Laminar Poisseulli flow been proposed by some author (Yu and Kawaguchi, 2002; Nie et al, 2000)
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