An Efficient and Robust Numerical Scheme for the SIMPLER Algorithm on Non-Orthogonal Curvilinear Coordinates: CLEARER

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Abstract
In this article, an Improved SIMPLER (CLEARER) algorithm is formulated to solve the incompressible fluid flow and heat transfer on the nonstaggered, nonorthogonal curvilinear grid system. By virtue of a modified momentum interpolation method in calculating the interface contravariant velocity in both the predictor step and the corrector step, the coupling between pressure and velocity is fully guaranteed, and the conservation law is also satisfied. A second relaxation factor is introduced in the corrector step, of which the convergent solution is independent. By setting the second relaxation factor less than the underrelaxation factor for the velocity to some extent, both the convergence rate and robustness can be greatly enhanced. Meanwhile, the CLEARER algorithm can also overcome the severe grid nonorthogonality. With the simplified pressure-correction equation, the convergent solution can still be obtained even when the intersection angle among grid lines is as low as 1°, which may provide valuable guidance in studying the fluid flow in complex geometries.

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