The goal of this paper is to construct discretizations for the equations of Lagrangian gas dynamics that preserve plane, cylindrical, and spherical symmetry in the solution of the original differential equations. The new method uses a curvilinear grid that is reconstructed from a given logically rectangular distribution of nodes. The sides of the cells of the reconstructed grid can be segments ...

The Finite Volume method is well adapted to the computation of the solution of pdes which are conservation (or balance) laws, for the reason that it respects the property of conservation of the pde under study. The mathematical analysis of the application of the Finite Volume method to hyperbolic first-order conservation laws can be dated from the mid sixties (see [TS62] for example). Concernin...

We introduce the coarsening of finite element computational grid strategy into the method proposed by Kačur and Mikula in [11] for the numerical solution of the Perona–Malik model modified in the sense of Catté, Lions, Morel and Coll. It improves the efficiency of the method, while the solution tends to be more flat during the selective smoothing process applied to the image. The numerical appr...

R -package ReacTran (Soetaert and Meysman 2009) contains functions to solve reactivetransport equations, as used e.g. in the environmental sciences. Essentially, it 1. Provides functions that subdivide the spatial extent into a number of discrete grid cells. 2. Approximates the advective-diffusive transport term by finite differences or finite volumes. The main package vignette (Soetaert and Me...

A parameterization for the motion of ice-shelf fronts on a Cartesian grid in finite-difference land-ice models is presented. The scheme prevents artificial thinning of the ice shelf at its edge, which occurs due to the finite resolution of the model. The intuitive numerical implementation diminishes numerical dispersion at the ice front and enables the application of physical boundary condition...

An affine finite element scheme approximation of a time dependent linear convectiondiffusion-reaction problem in 2D and 3D is presented. Specific conditions are given in terms of the coefficient functions, the computational grid and the discretization parameters to ensure that the nonnegativity property of the true solution is also satisfied by its approximation. Numerical examples are given wh...

Interpolation of field data from unstructured meshes requires the potentially expensive identification of the finite element or volume within which the interpolating point lies. A number of geometric search algorithms have been proposed to reduce this expense at the cost of setting up and storing additional search tables. Using tetrahedral finite element models we show that a structured auxilia...

A 3rd order numerical model is developed for global advection transport computation. The multi-moment finite volume method has been implemented to the hexagonal-pentagonal geodesic grid for spherical geometry. Two kinds of moments, i.e. point value and volume-integrated average, are used as the constraint conditions to derive the time evolution equations to update the computational variables, w...

Finite-difference time-domain (FDTD) grids are often described as being divergence-free in a source-free region of space. However, in the presence of a source, the continuity equation states that charges may be deposited in the grid, while Gauss’s law dictates that the fields must diverge from any deposited charge. The FDTD method will accurately predict the (diverging) fields associated with c...

Today, many global spectral models apply the reduced grid (i.e. the grid where the number of points in longitude is gradually reduced while approaching the poles). The construction of the global finite-difference semi-Lagrangian SL-AV model [1] enables the implementation of the reduced grid: some part of calculations is carried out in space of Fourier coefficients in longitude. Also, the semi-L...