The semi-Lagrangian transport method was introduced into atmospheric modeling by Robert, Henderson, and Turnbull. A set of test problems, standard for the shallow water equations on a sphere, are solved and results compared with an Eulerian spectral model. This form is particularly well suited for numerical computations using a semi-Lagrangian spectral discretization. A new formulation of the shallow water equations is derived which exhibits an advective form for the vorticity and divergence. The shallow water equations modeling flow on a sphere are useful for the development and testing of numerical algorithms for atmospheric climate and weather models.
#Tracer dmg verification
Simulation results include a simple proof of concept, verification using a manufac- tured solution, and fragmentation of a uniformly loaded thin ring that clearly demonstrates the improvement offered by the ALE LMT = , A detailed description of the algorithm is provided along with discussion of its computational aspects. The focus of this work is an ALE method that incorporates transport of variables on discrete, massless points that move with the velocity field, referred to as Lagrangian material tracers (LMT), and consequently prevents diffusion of certain material quantities of interest.
This drawback poses great difficulty for applications of material failure for which discrete features are important, but are smeared out as a result of the diffusive advection op- eration. Despite the advantages of using ALE for such problems, the method is associ- ated with diffusion of material quantities due to the advection transport step of the computa- tional cycle.
ALE computations are highly desirable for simulating dynamic problems that incorporate multiple materials and large deformations. A method for providing non-diffuse transport of material quantities in arbitrary Lagrangian- Eulerian (ALE) dynamic solid mechanics computations is presented.
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