55 research outputs found
A realizability-preserving high-order kinetic scheme using WENO reconstruction for entropy-based moment closures of linear kinetic equations in slab geometry
We develop a high-order kinetic scheme for entropy-based moment models of a
one-dimensional linear kinetic equation in slab geometry. High-order spatial
reconstructions are achieved using the weighted essentially non-oscillatory
(WENO) method, and for time integration we use multi-step Runge-Kutta methods
which are strong stability preserving and whose stages and steps can be written
as convex combinations of forward Euler steps. We show that the moment vectors
stay in the realizable set using these time integrators along with a maximum
principle-based kinetic-level limiter, which simultaneously dampens spurious
oscillations in the numerical solutions. We present numerical results both on a
manufactured solution, where we perform convergence tests showing our scheme
converges of the expected order up to the numerical noise from the numerical
optimization, as well as on two standard benchmark problems, where we show some
of the advantages of high-order solutions and the role of the key parameter in
the limiter
Second-order mixed-moment model with differentiable ansatz function in slab geometry
We study differentiable mixed-moment models (full zeroth and first moment,
half higher moments) for a Fokker-Planck equation in one space dimension.
Mixed-moment minimum-entropy models are known to overcome the zero net-flux
problem of full-moment minimum entropy models. Realizability theory for
these modification of mixed moments is derived for second order. Numerical
tests are performed with a kinetic first-order finite volume scheme and
compared with , classical and a reference scheme.Comment: arXiv admin note: text overlap with arXiv:1611.01314,
arXiv:1511.0271
Perturbed, Entropy-Based Closure for Radiative Transfer
We derive a hierarchy of closures based on perturbations of well-known
entropy-based closures; we therefore refer to them as perturbed entropy-based
models. Our derivation reveals final equations containing an additional
convective and diffusive term which are added to the flux term of the standard
closure. We present numerical simulations for the simplest member of the
hierarchy, the perturbed M1 or PM1 model, in one spatial dimension. Simulations
are performed using a Runge-Kutta discontinuous Galerkin method with special
limiters that guarantee the realizability of the moment variables and the
positivity of the material temperature. Improvements to the standard M1 model
are observed in cases where unphysical shocks develop in the M1 model.Comment: 35 pages, 8 figure
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