A second-order accurate pressure correction scheme for viscous incompressible flow
SIAM Journal on Scientific and Statistical Computing
Comparison of finite-volume numerical methods with staggered and colocated grids
Computers and Fluids
Inertial manifolds and multigrid methods
SIAM Journal on Mathematical Analysis
Applications of inertial manifolds to scientific computing: a new insight in multilevel methods
Trends and perspectives in applied mathematics
Multilevel methods for the simulation of turbulence: a simple model
Journal of Computational Physics
Applied Numerical Mathematics
Incremental unknowns for solving the incompressible Navier—Stokes equations
Mathematics and Computers in Simulation
Time Marching Multilevel Techniques for Evolutionary Dissipative Problems
SIAM Journal on Scientific Computing
Journal of Scientific Computing
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This article is intended as a preliminary report on the implementation of a finite volume multilevel scheme for the discretization of the incompressible Navier---Stokes equations. As is well known the use of staggered grids (e.g. MAC grids, Peri驴 et al. Comput. Fluids, 16(4), 389---403, (1988)) is a serious impediment for the implementation of multilevel schemes in the context of finite differences. This difficulty is circumvented here by the use of a colocated finite volume discretization (Faure et al. (2004a) Submitted, Peri驴 et al. Comput. Fluids, 16(4), 389---403, (1988)), for which the algebra of multilevel methods is much simpler than in the context of MAC type finite differences. The general ideas and the numerical simulations are presented in this article in the simplified context of a two-dimensional Burgers equations; the two-, and three-dimensional Navier---Stokes equations introducing new difficulties related to the incompressibility condition and the time discretization, will be considered elsewhere (see Faure et al. (2004a) Submitted and Faure et al. (2004b), in preparation).