Numerical schemes that can sustain good accuracy over coarse mesh size are of increasing interest, as traditional fine-mesh methods generally take too much time to reach desirable accuracy for integral, multi-physics simulations in engineering applications. Modified Nodal Integral Method (MNIM), one of the coarse-mesh methods, was developed for the 2D and 3D Navier-Stokes equations. It shows high accuracy even with very coarse meshes. However, the local transverse integration procedure required to obtain the set of ordinary differential equations for each cell limits the MNIM to fluid flow fields that, in 2D, can be decomposed into rectangular-shaped cells. As a result, the efficiency achieved by using coarse meshes is adversely impacted due to the need to use finer rectangular cells for problems with complex boundaries. In an effort to release the above-mentioned restriction, we are applying a simple isoparametric geometry mapping approach, which has been widely used in finite volume and finite element methods, to incorporate irregular quadrilateral elements into MNIM for the two-dimensional, time-dependent, in-compressible Navier-Stokes equations. 
Mapping of the quadrilateral element to a (2 x 2) square element |