SciCADE 2013
International Conference on Scientific Computation and Differential Equations
September 16-20, 2013, Valladolid (Spain)

Contributed Talk

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Stable and efficient simulation of PDAEs describing flow networks

C. Huck, C. Tischendorf and L. Jansen

Abstract
We are interested in partial differential algebraic equations (PDAEs) describing flow networks. These PDAEs consist of hyperbolic PDEs of the type$p_t&+Am_x=0 m_t&+Bp_x+H+G(m)m=0$ which are coupled with algebraic boundary conditions. For our simulation approach we use the method of lines, yielding a differential algebraic equation (DAE) which is adaptively discretized in time. We present a perturbation analysis for a simplified prototype motivated by the system above for different types of space discretizations. In particular we will show that the index of the resulting DAEs may depend on the chosen space discretization. Additionally, we present a network topologically dependent space discretization guaranteeing DAEs of index 1. Furthermore we study a network topological procedure to reduce the resulting DAEs into semi-explicit systems of the form$x^{\prime}&=f(x,t) y&=Mx+r(t).$

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