A conservative adaptive projection method for the variable density incompressible Navier-Stokes equations. (English) Zbl 0933.76055

We present a method for solving the equations governing time-dependent, variable density incompressible flow in two or three dimensions on an adaptive hierarchy of grids. The method is based on a projection formulation in which we first solve advection-diffusion equations to predict intermediate velocities, and then project these velocities onto a space of approximately divergence-free vector fields. Our treatment of the first step uses a specialized second-order upwind method for differencing the nonlinear convection terms that provides a robust treatment of these terms suitable for inviscid and high Reynolds number flow. Density and other scalars are advected in such a way as to maintain conservation, if appropriate, and free-stream preservation. Numerical examples demonstrate the algorithms’s accuracy and convergence properties. \(\copyright\) Academic Press.


76M20 Finite difference methods applied to problems in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids


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