Exploiting Tensor Structure in Kinetic Equations: General Framework
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Kinetic models for fluid dynamics have gained popularity over the years. In contrast to standard models, they are valid in the full range of modern applications in science and industry, from gas flows near vaccum to high Mach number flows. However, the numerical solution of these models requires the discretization of the six dimensional phase space, the product of position and velocity space. This has limited the use of higher order discretization in applications, particularly for domains with complicated geometry. In this talk, we exploit the special structure of kinetic equations to decouple spatial and velocity dependencies during assembly and the solution of linear systems appearing in Quasi Newton methods. We argue that the most challenging part of kinetic equations is not the collision mechanism but boundary conditions as they couple space and velocity in a nonseparable way. An application of the tensor framework to the Boltzmann equation discretized by the method moments closes the talk.
