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The multiscale patch scheme is built from given small micro-scale simulations of complicated physical processes to empower large macro-scale simulations. By coupling small patches of simulations over unsimulated spatial gaps, large savings in computational time are possible. Here we discuss generalising the patch scheme to the case of wave systems on staggered grids in 2D space. Classic macro-scale interpolation provides a generic coupling between patches that achieves arbitrarily high order consistency between the emergent macro-scale simulation and the underlying micro-scale dynamics. Eigen-analysis indicates that the resultant scheme empowers feasible computation of large macro-scale simulations of wave systems even with complicated underlying physics. As examples we use the scheme to simulate some wave scenarios via a turbulent shallow water model.
In the present manuscript, we consider the problem of dispersive wave simulation on a rotating globally spherical geometry. In this Part IV, we focus on numerical aspects while the model derivation was described in Part III. The algorithm we propose
An efficient method for the calculation of ferromagnetic resonant modes of magnetic structures is presented. Finite-element discretization allows flexible geometries and location dependent material parameters. The resonant modes can be used for a sem
The regularisation of nonlinear hyperbolic conservation laws has been a problem of great importance for achieving uniqueness of weak solutions and also for accurate numerical simulations. In a recent work, the first two authors proposed a so-called H
Vortical flows in shallow water interact with long surface waves by virtue of the nonlinear terms of the fluid equations. Analytical formulae are derived that quantify the spontaneous generation of such waves by unsteady vorticity as well as the scat
In this paper, we introduce a new extended version of the shallow water equations with surface tension which is skew-symmetric with respect to the L2 scalar product and allows for large gradients of fluid height. This result is a generalization of th