### Zakharov A. Димитриенко Ю.И. Коряков М.Н.

## Mathematical modeling of nonequilibrium gas-dynamic processes by RKDG method

### Reporter: Zakharov A.

This paper studies the RKDG (Runge-Kutta Discontinuous Galerkin) finite element method for numerical simulation of hypersonic nonequilibrium gas flows. We consider the Navier-Stokes equations with chemical kinetics. Integration of the Navier-Stokes equations is performed by the splitting into physical processes. At the first stage the members of the viscous terms are excluded from the consideration. The problem is solved for ideal gas. Then the viscous term components are taken into account but do not take into account convection. Further the equations of chemical kinetics are solved in 3 stages. Firstly, an explicit-implicit scheme is used to solve the system of difference equations with source terms. Then the convection of the chemical components is taken into account. The system is solved by the RKDG method similarly the step of solving of inviscid flow. And then the diffusion of chemical components is taken into account. The algorithm for solving the equations is similarly the step of solving of viscous components. The results of a simulation of flow about a spherical nose segment of a model hypersonic aircraft are presented.

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