In this paper we present a method for solving the time-dependent incompressible Euler equations on an adaptive grid. The method is based on a projection formulation in which we first solve convection equations to predict intermediate velocities, and then project these velocities onto a space of approximately divergence-free vector fields. Our treatment of the convection step uses a specialized ...

An integration algorithm that conjugates a Method of Lines (MOL) strategy based on finite differences space discretizations, with a collocation strategy based on increasing level dyadic grids is presented. It reveals potential either as a grid generation procedure and a Partial Differential Equation (PDE) integration scheme. It copes satisfactorily with a example characterized by a steep travel...

An adaptive finite element strategy is employed to solve the Perona-Malik model as modified by Catté, Lions, Morel and Coll for image processing by (often highly) nonlinear diffusion. FEMLAB® and MATLAB® are used to implement the experiments and they prove to be very suitable tools to run this type of problem. Refinement and coarsening of the grids are used as needed and the approach leads to u...

The weak Lagrange–Galerkin finite element method for the two-dimensional shallow water equations on adaptive unstructured grids is presented. The equations are written in conservation form and the domains are discretized using triangular elements. Lagrangian methods integrate the governing equations along the characteristic curves, thus being well suited for resolving the non-linearities introd...

We test the behavior of a unified continuous/discontinuous Galerkin (CG/DG) shallow water model in spherical geometry with curved elements on three different grids of ubiquitous use in atmospheric modeling: (A) the cubed-sphere, (B) the reduced latitude-longitude, and (C) the icosahedral grid. Both conforming and non-conforming grids are adopted including static and dynamically adaptive grids f...

We present a method of adaptive grid refinement for the solution of the steady Euler equations for transonic flow. Our algorithm automatically decides where the coarse grid accuracy Is insufficient, and creates locally uniform refined grids in these regions. This typically occurs at the leading and trailing edges. The solution is then integrated to steady state using the same integrator (FLO52)...

In this paper we present a graph grammar based direct solver algorithm for hp-adaptive finite element method simulations with point singularities. The solver algorithm is obtained by representing computational mesh as a graph and prescribing the solver algorithm by graph grammar productions. Classical direct solvers deliver O(Np+N) computational cost for regular 2D grids, and O(Np+N) for regula...

An integrated tool developed for the construction of unstructured numerical grids about complex configurations is presented. The tool is highly integrated and employs the native underlying geometry modeling kernel used to define the target domain for providing topological and geometric access used by the grid generation procedures. This access greatly reduces the overall process time required t...

A narrow-band-based adaptive level set method is proposed for mesh evolution in this paper. In the preprocessing step, the portions of the mesh with high curvature are detected and clustered as fine geometric details. Then the fine grids with optimal orientations are defined for each detected portions, while the coarse grid is chosen for global evolution. The solutions on different scale grids ...

This paper summarizes a method that solves both the three dimensional thin-layer Navier-Stokes equations and the Euler equations using overset structured and solution adaptive unstructured grids with applications to helicopter rotor fiowfields. The overset structured grids use an implicit finite-difference method to solve the thin-layer Navier-Stokes/Euler equations while the unstructured grid ...