Parallel computation of unsteady compressible flows with the EDICT

Recently, the Enhanced-Discretization Interface-Capturing Technique (EDICT) was introduced for simulation of unsteady flow problems with interfaces su ch as two-fluid and free-surface flows. The EDICT yields increased accuracy in representing the interface. Here we extend the EDICT to simulation of u nsteady viscous compressible flows with boundary/shear layers and shock/exp ansion waves. The purpose is to increase the accuracy in selected regions o f the computational domain. An error indicator is used to identify these re gions that need enhanced discretization. Stabilized finite-element formulat ions are employed to solve the Navier-Stokes equations in their conservatio n law form. The finite element functions corresponding to enhanced discreti zation are designed to have two components, with each component coming from a different level of mesh refinement over the same computational domain. T he primary component comes from a base mesh. A subset of the elements in th is base mesh are identified for enhanced discretization by utilizing the er ror indicator. A secondary, more refined, mesh is constructed by patching t ogether the second-level meshes generated over this subset of elements, and the second component of the functions comes from this mesh. The subset of elements in the base mesh that form the secondary mesh may change from one time level to other depending on the distribution of the error in the compu tations.