A Fourth-Order Accurate Method for the Incompressible Navier-Stokes Equations on Overlapping Grids

• Published in: Journal of computational physics 1994-07, Vol.113 (1), p.13-25
• Main Author: Henshaw, William D.
• Format: Article
• Language: English
• Subjects: 990200 > Mathematics & Computers; ACCURACY; Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Computational methods in fluid dynamics; Computational techniques; COMPUTERIZED SIMULATION; DIFFERENTIAL EQUATIONS; ENGINEERING; EQUATIONS; Exact sciences and technology; Finite-difference methods; Fluid dynamics; FLUID FLOW; Fluid mechanics: general mathematical aspects; Fundamental areas of phenomenology (including applications); GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; INCOMPRESSIBLE FLOW; Mathematical methods in physics; MESH GENERATION; NAVIER-STOKES EQUATIONS; Numerical approximation and analysis; NUMERICAL SOLUTION; Ordinary and partial differential equations, boundary value problems; PARTIAL DIFFERENTIAL EQUATIONS; Physics; SIMULATION 420400 > Engineering-- Heat Transfer & Fluid Flow
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1006/jcph.1994.1114

A method is described to solve the time-dependent incompressible Navier-Stokes equations with finite differences on curvilinear overlapping grids in two or three space dimensions. The scheme is fourth-order accurate in space and uses the momentum equations for the velocity coupled to a Poisson equation for the pressure. The boundary condition for the pressure is taken as ∇ • u = 0. Extra numerical boundary conditions are chosen to make the scheme accurate and stable. The velocity is advanced explicitly in time; any standard time stepping scheme such as Runge-Kutta can be used. The Poisson equation is solved using direct or iterative sparse matrix solvers or by the multigrid algorithm. Computational results in two and three space dimensions are given.