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On numerical solution of compressible flow in time-dependent domains. (English) Zbl 1249.65196
The paper is concerned with the numerical solution of a compressible flow in a bounded domain $$\Omega _t\subset \mathbb {R}^2, t\in [0,T];$$ with a boundary $$\partial \Omega _t=\Gamma _{I}\cup \Gamma _O\cup \Gamma _{W_t}.$$ The system consisting of the continuity equation, the Navier-Stokes equations and the energy equation can be written in the form $\frac {\partial \mathbf {w}}{\partial t}+\sum _{s-1}^2\frac {\partial \mathbf {f}_s(\mathbf {w})}{\partial x_s} =\sum _{s-1}^2\frac {\partial R_s(\mathbf {w},\nabla \mathbf {w})}{\partial x_s},\;\mathbf {w}=(w_1,w_2,w_3,w_4)^T$ with the initial condition $$\mathbf {w}(x,0)=\mathbf {w}^0(x),\;x\in \Omega _0$$ and the boundary conditions on the inlet $$\Gamma _I$$, the outlet $$\Gamma _O$$ and the impermeable walls $$\Gamma _{W_t}$$.
The discontinuous Galerkin finite element method is used for the space discretization. The time discretization is carried out with the aid of a linearized semi-implicit method.

##### MSC:
 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 76M10 Finite element methods applied to problems in fluid mechanics 76N15 Gas dynamics (general theory)
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