Spatial Differencing for Finite Difference Codes

摘要

We derive new expressions for the approximation of the spatial gradients of velocity for use in finite difference programs for solid and fluid dynamics. Analytically, the change of volume of a finite body can be determined from the velocity on the surface of the body. Our expressions are found essentially by enforcing this relation on the difference approximations. For problems with cylindrical symmetry, the new forms are substantially different than any we have previously seen. The advantages of the new forms are demonstrated in a sample calculation. (ERA citation 10:022138)