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For piecewise constant magnetic fields, the Bloch equations (without relaxation terms) can be solved explicitly.
Second, stiff relaxation terms are solved with a Newton method that also guarantees positivity and robustness.
To model more physical phenomena we have to introduce phenomenological relaxation terms.
The relaxation terms are then added which are compatible with the entropy inequality.
It results in a single velocity, non-conservative hyperbolic model with two energy equations involving relaxation terms.
Many hyperbolic systems of equations with stiff relaxation terms reduce to a parabolic description when relaxation dominates.
Similar(30)
In this model each coupling is added as an extra relaxation term in the collision operator.
However, the colliding relaxation term have a little influence on the kernel region in the startup process for Kn ≥ 0.1.
A relaxation term is added when it comes to the design of an iterative solver for the nonlinear system.
We propose to penalize the nonlinear collision term by a BGK-type relaxation term, which can be solved explicitly even if discretized implicitly in time.
Due to the multiple temperature approximation, the second viscosity coefficient in the Navier Stokes equations is replaced by the temperature relaxation term.
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