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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.

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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