Accurate Conservative Remapping (Rezoning) for Arbitrary Lagrangian-Eulerian Computations

The Arbitrary Lagrangian-Eulerian (ALE) method in computational fluid dynamics requires the periodic remapping of conserved quantities such as mass, momentum, and energy from a Lagrangian mesh to some other arbitrarily defined mesh. This procedure is a type of interpolation which is usually constrained to be conservative and monotone. It is typically carried out by solving a partial differential equation analogous to the continuity equation. Alternatively, the remapping may be carried out using an integral formulation which is (for the remapping of mass) \ mₖ = ₕ䂵 ({ r) dV, } \ where mₖ is the mass of a cell k of the new mesh whose volume is Vₖ, and (r) is the known density distribution on the old (Lagrangian) mesh. Remapping using this integral method avoids many drawbacks of the continuous method but the evaluation of such integrals is costly and difficult for arbitrary meshes. Recently, very efficient methods 6, 7 have been demonstrated for the case of constant cell density in two dimensions. We now extend these methods to the much more accurate case in which the density distribution in linear within each cell. This results in second order accuracy. However, to preserve monotonicity the gradients are limited using the option of two simple local limiters. To the extent that the limiting is applied the method locally reverts to first order accuracy.