In this paper we present an extension of Residual Distribution techniques for the simulation of compressible flows in non-equilibrium conditions. The latter are modeled by means of a state-of-the-art multi-species and two-temperature model.
An entropy-based variable transformation that symmetrizes the projected advective Jacobian for such a thermophysical model is introduced. Moreover, the transformed advection Jacobian matrix presents a block diagonal structure, with mass-species and electronic-vibrational energy being completely decoupled from the momentum and total energy sub-system.
The advantageous structure of the transformed advective Jacobian can be exploited by contour-integration-based Residual Distribution techniques: established schemes that operate on dense matrices can be substituted by the same scheme operating on the momentum–energy subsystem matrix and repeated application of scalar scheme to the mass-species and electronic-vibrational energy terms.
Finally, the performance gain of the symmetrizing-variables formulation is quantified on a selection of representative testcases, ranging from subsonic to hypersonic, in inviscid or viscous conditions.
In this paper we present an extension of Residual Distribution techniques for the simulation of compressible flows in non-equilibrium conditions. The latter are modeled by means of a state-of-the-art multi-species and two-temperature model.
An entropy-based variable transformation that symmetrizes the projected advective Jacobian for such a thermophysical model is introduced. Moreover, the transformed advection Jacobian matrix presents a block diagonal structure, with mass-species and electronic-vibrational energy being completely decoupled from the momentum and total energy sub-system.
The advantageous structure of the transformed advective Jacobian can be exploited by contour-integration-based Residual Distribution techniques: established schemes that operate on dense matrices can be substituted by the same scheme operating on the momentum–energy subsystem matrix and repeated application of scalar scheme to the mass-species and electronic-vibrational energy terms.
Finally, the performance gain of the symmetrizing-variables formulation is quantified on a selection of representative testcases, ranging from subsonic to hypersonic, in inviscid or viscous conditions. Read More
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