Simulation of time-dependent flow in cavities with the additive-correction multigrid method .1. Mathematical formulation

A time-accurate, additive-correction multigrid method for the prediction of two-dimensional unsteady flows is presented in this article. The method makes use of the additive-correction multigrid strategy, which, originally proposed for steady-flow problems, is extended to the calculation of time-dependent and chaotic flows at high Reynolds or Rayleigh numbers. The numerical algorithm guarantees absolute, to machine accuracy, mass conservation at every time step, and it is characterized by second-order accuracy in space and time. In a companion article [I], the method is applied to the calculation of unsteady flow in cavities, i.e., the lid-driven cavity problem at high Reynolds number, and the buoyant flow in differentially heated cavities at high values of the Rayleigh number. Although the method has been implemented and tested for two-dimensional flows, a can also be extended to three-dimensional problems.