A SVD-GFD scheme for computing 3D incompressible viscous fluid flows

A generalized finite difference (GFD) scheme for the simulation of three-dimensional (3D) incompressible viscous fluid flows in primitive variables is described in this paper. Numerical discretization is carried out on a hybrid Cartesian cum meshfree grid, with derivative approximation on non-Cartesian grids being carried out by a singular value decomposition (SVD) based GFD procedure. The Navier–Stokes equations are integrated by a time-splitting pressure correction scheme with second-order Crank–Nicolson and second-order discretization of time and spatial derivatives respectively. Axisymmetric and asymmetric 3D flows past a sphere with Reynolds numbers of up to 300 are simulated and compared with the results of Johnson and Patel [Johnson TA, Patel VC. Flow past a sphere up to a Reynolds number of 300. J Fluid Mech 1999;378:19–70] and others. Flows past toroidal rings are also simulated to illustrate the ability of the scheme to deal with more complex body geometry. The current method can also deal with flow past 3D bodies with sharp edges and corners, which is shown by a simple 3D case.