Question regarding non-uniform FVM staggered grid
I have a question regarding non-uniform FVM staggered Cartesian grid.
When the grid is non-uniform, I believe there are 2 ways to discretize the volume of the u/v grid, assuming the p grid is created.
1. The east/west faces of the u grid intersects the cell center of p. In that case, the distance of the east/west faces from the cell center of u will be different. the volume of u and p cells are different.
2. The west face of the u grid intersects the cell center of p but the east face does not. The volume of the u cell and p cell are equal, except shifted. In that case, the distance of the east/west faces from the cell center of u will be different.
Are these 2 discretizations sound? Is there any preferences of one over another?
I think there's a real advantage in having the cell faces coincide with the p locations (cell centers). Try a simple one-d steady state heat conduction problem as an easy-to-derive example. With fixed temperatures at each end, this problem has a simple analytic solution. Expand your two differencing choices in Taylor series and example the lower-order terms that you truncate. One of the two choices will have a leading truncated term that grows as 1 over dt for a non-uniform mesh!
thanks for your explanation.
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