An accurate numerical solution algorithm for 3D velocity-vorticity Navier-Stokes equations by the DQ method

作者：Lo DC; Young DL^*; Murugesan K

来源：Communications in Numerical Methods in Engineering, 2006, 22(3): 235-250.

DOI：10.1002/cnm.817

• velocity-vorticity Navier-Stokes equations
• differential quadrature method

A numerical scheme based on a differential quadrature (DQ) method is discussed for the solution of three-dimensional velocity-vorticity Navier-Stokes equations. Numerical solutions of the six field variables, three velocities and three vorticities are obtained by adopting a Coupled numerical solution procedure. Hence, it is required to specify only the velocity boundary conditions, whereas the vorticity values at the boundary are Computed implicitly, thus without seeking boundary vorticity values by an iterative procedure followed in other explicit numerical schemes. Since the DQ method approximates a given differential operator with higher-order polynomials, the vorticity definition is accurately enforced at the boundary. This ensures a divergence-free Solution for the flow field. Flow simulations obtained for a lid-driven cubic cavity for Stokes flow and Re = 100, 400 and 1000 show excellent agreements with other numerical schemes. A grid independence study demonstrates that the present numerical scheme could predict benchmark Solutions with coarser meshes than other numerical schemes.

• 出版日期2006-3