Multidimensional upwind scheme of diagonal Cartesian method for an advection–diffusion problem

The natural calculation region in fluid dynamics involves complex boundaries. When using the Cartesian grid to approximate complex boundaries, two difficulties develop: the boundary zigzag effect and disagreement of direction of grid line and velocity. The multidimensional upwind scheme of the diagonal Cartesian method (DCM), using both Cartesian grid lines and diagonal lines segments, is presented in this paper to simulate the complex boundaries of the multiple-layer quasi 3D model equations. The DCM improves the simulation accuracy for the boundaries and calculation time increases only slightly compared to the Cartesian method. In order to verify the new scheme, a test case is presented which rotates the cavity flow at 45° to compare the numerical calculation results at different Reynolds numbers. The test case shows that the scheme is accurate and efficient in improving the simulation results. Then the three-dimensional advection–diffusion processes in the tidal water of the Hongyanhe Power Plant are simulated using this model. Numerical results show that the scheme is not only efficient on an experiment basis, but also efficient and reliable when applied to a large scale natural water area.