Finite Difference Method on Triangulated Random Mesh.
Hiroshi Koibuchi · TRANSACTIONS OF THE JAPAN SOCIETY OF MECHANICAL ENGINEERS Series B · 1991
Partial differential equations are discretized on a triangulated random mesh in two dimensions. As a first example to test our discretizations, a Laplace's equation with Dirichlet's boundary conditions on a square area is solved on two types of triangulated mesh. The results are compared with those of the regular sguare mesh. The second example is a discretization of Navier-Stokes equations for a standard cavity problem of incompressible viscous flow. For the region of low Reynolds number, the unsteady equations are iterated on two types of triangulated random mesh and a regular square mesh, as in the first example. Our tentative conclusion is that for many problems, our finite difference method on a triangulated random mesh can lead to the same results as those obtained by the use of a regular square mesh.