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We study the possibility for the implementation of linear wave structures on discrete grids with various dimensions. The systems of the first order differential equations for the set of virtual functions, describing the wave propagation, are derived for different spectral zones. We are particularly interested in the spectral regions which are localized near the lowest and the maximal frequencies, as well as in the vicinity of a central frequency. The cases of discrete orthogonal grids with dimensions from 1 to 4 are analyzed. The possibility of the propagation of waves in the considered situations is substantiated by numerical simulations.
We develop a general framework for designing conservative numerical methods based on summation by parts operators and split forms in space, combined with relaxation Runge-Kutta methods in time. We apply this framework to create new classes of fully-d
This paper explores Tadmors minimum entropy principle for the relativistic hydrodynamics (RHD) equations and incorporates this principle into the design of robust high-order discontinuous Galerkin (DG) and finite volume schemes for RHD on general mes
In this paper, we develop a new free-stream preserving (FP) method for high-order upwind conservative finite-difference (FD) schemes on the curvilinear grids. This FP method is constrcuted by subtracting a reference cell-face flow state from each cel
An approach to calculating approximate solutions to the continuum Schwinger-Dyson equations is outlined, with examples for phi^4 in D=1. This approach is based on the source Galerkin methods developed by Garcia, Guralnik and Lawson. Numerical issues
In this work, we propose and develop efficient and accurate numerical methods for solving the Kirchhoff-Love plate model in domains with complex geometries. The algorithms proposed here employ curvilinear finite-difference methods for spatial discret