56 research outputs found

    von Neumann Stability Analysis of Globally Constraint-Preserving DGTD and PNPM Schemes for the Maxwell Equations using Multidimensional Riemann Solvers

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    The time-dependent equations of computational electrodynamics (CED) are evolved consistent with the divergence constraints. As a result, there has been a recent effort to design finite volume time domain (FVTD) and discontinuous Galerkin time domain (DGTD) schemes that satisfy the same constraints and, nevertheless, draw on recent advances in higher order Godunov methods. This paper catalogues the first step in the design of globally constraint-preserving DGTD schemes. The algorithms presented here are based on a novel DG-like method that is applied to a Yee-type staggering of the electromagnetic field variables in the faces of the mesh. The other two novel building blocks of the method include constraint-preserving reconstruction of the electromagnetic fields and multidimensional Riemann solvers; both of which have been developed in recent years by the first author. We carry out a von Neumann stability analysis of the entire suite of DGTD schemes for CED at orders of accuracy ranging from second to fourth. A von Neumann stability analysis gives us the maximal CFL numbers that can be sustained by the DGTD schemes presented here at all orders. It also enables us to understand the wave propagation characteristics of the schemes in various directions on a Cartesian mesh. We find that the CFL of DGTD schemes decreases with increasing order. To counteract that, we also present constraint-preserving PNPM schemes for CED. We find that the third and fourth order constraint-preserving DGTD and P1PM schemes have some extremely attractive properties when it comes to low-dispersion, low-dissipation propagation of electromagnetic waves in multidimensions. Numerical accuracy tests are also provided to support the von Neumann stability analysis

    Lagrangian ADER-WENO Finite Volume Schemes on Unstructured Triangular Meshes Based On Genuinely Multidimensional HLL Riemann Solvers

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    In this paper we use the genuinely multidimensional HLL Riemann solvers recently developed by Balsara et al. to construct a new class of computationally efficient high order Lagrangian ADER-WENO one-step ALE finite volume schemes on unstructured triangular meshes. A nonlinear WENO reconstruction operator allows the algorithm to achieve high order of accuracy in space, while high order of accuracy in time is obtained by the use of an ADER time-stepping technique based on a local space-time Galerkin predictor. The multidimensional HLL and HLLC Riemann solvers operate at each vertex of the grid, considering the entire Voronoi neighborhood of each node and allows for larger time steps than conventional one-dimensional Riemann solvers. The results produced by the multidimensional Riemann solver are then used twice in our one-step ALE algorithm: first, as a node solver that assigns a unique velocity vector to each vertex, in order to preserve the continuity of the computational mesh; second, as a building block for genuinely multidimensional numerical flux evaluation that allows the scheme to run with larger time steps compared to conventional finite volume schemes that use classical one-dimensional Riemann solvers in normal direction. A rezoning step may be necessary in order to overcome element overlapping or crossing-over. We apply the method presented in this article to two systems of hyperbolic conservation laws, namely the Euler equations of compressible gas dynamics and the equations of ideal classical magneto-hydrodynamics (MHD). Convergence studies up to fourth order of accuracy in space and time have been carried out. Several numerical test problems have been solved to validate the new approach

    The morphology of and locations of star formation in impact induced ring galaxies

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    Observed ring galaxies appear to fall into two major types. The first tends to consist of isolated galaxies which display a smooth, apparently circular ring and a central nucleus. These have been variously classified as R(S) by de Vaucouleurs (1959) and as type O by Few and Madore (1986). The second class of ring galaxy nearly always has a close companion of comparable size (no less than about one tenth that of the ring galaxy). In these objects the ring is knotty in appearance, is usually elliptical, even when deprojected on the sky, and is often open on one side, having a 'horse shoe' or 'banana' shape. The nucleus does not usually appear at the center of the ring and is sometimes apparently absent, giving rise to an 'empty ring' galaxy. deVaucouleurs et al. (1976) designated this second type as RING, while Few and Madore (1986) have classified similar galaxies as P type. These galaxies have elevated far IR emission, bright HII regions, and blue spectral colors. The different environments of the two types or ring galaxy, together with their overall morphological and spectral differences suggest that the R(S)/O type are most probably the result of an instability that occurs in isolated galaxies, whereas the RING/P type appears to be the result of a recent collision between two roughly equal mass objects, at least one of which is a disk galaxy. Theys and Spiegel (1976) studied a sample of this latter type and identified three subclasses: RE: galaxies with crisp, empty rings; RN: galaxies like those of RE but with off-center nuclei; RK: galaxies having single dominant knots or condensations in the rings. A presentation of a preliminary understanding of the connections between these different observed forms in terms of parameters which are intrinsic to the galaxy system, such as time since collision and impact parameter, and in terms of our line of sight view is the purpose of this paper. Here we report results we have obtained from three dimensional computer simulations of collisions between equal mass galaxies, one of which is a rotating, disk galaxy containing both gas and stars and the other is an elliptical containing stars only. We have used a combined n-body/SPH program (see Balsara, 1990) to model fully self consistent models in which the halo mass is 2.5 times that of the disk and gas comprises ten percent of the disk mass
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