We review the spatial discretization procedure for three high-order, unstructured grid methods recently developed for use within ocean circulation modeling. They are based respectively on spectral finite element and high-order finite volume formulations. We discuss and contrast the three methods in the context of the shallow water equations.

A new volume deformation technique using FEM and voxel-texture (voxture) maps has been developed. In contrast to the traditional deformation techniques, the new algorithm is aimed at volume transformations, deformations and volume metamorphosis.

Abstract. We present a numerical scheme for the solution of a class of atmospheric models where high horizontal resolution is required while a coarser vertical structure is allowed. The proposed scheme considers a layering procedure for the original set of equations, and the use of high-order ADER finite volume schemes for the solution of the system of balance laws arising from the dimensional ...

The occurrence of unphysical negative concentrations in solutions to diffusion equations is a well known and severe problem. Especially in three dimensions finite element discretizations give qualitatively very poor results, while finite volume discretizations are much more stable. We investigate the cause of these instabilities and trace them back to constraints on the mesh. It turns out that ...

A general framework for weak residual error estimators applying to various types of boundary value problems in connection with finite element and finite volume approximations is developed. Basic ideas commonly shared by various applications in error estimation and adaptive computation are presented and illustrated. Some numerical results are given to show the effectiveness and efficiency of the...

A numerical method in which the Rankine-Hugoniot condition is enforced at the discrete level is developed. The simple format of central discretization in a finite volume method is used together with the jump condition to develop a simple and yet accurate numerical method free of Riemann solvers and complicated flux splittings. The steady discontinuities are captured accurately by this numerical...

We study spatially semidiscrete and fully discrete finite volume element methods for the homogeneous heat equation with homogeneous Dirichlet boundary conditions and derive error estimates for smooth and nonsmooth initial data. We show that the results of our earlier work [Math. Comp. 81 (2012), 1–20] for the lumped mass method carry over to the present situation. In particular, in order for er...

A “purely gasdynamic” indirect detonation initiation process is presented that can be independent of diffusion, viscosity and turbulence, and does not require direct initiation. In this process, energy is deposited into a finite volume of fluid in an amount of time that is similar to the acoustic timescale of the fluid volume. Highly resolved two-dimensional simulations show that the artificial...