A ROBUST CONSERVATIVE MIXED FINITE ELEMENT METHOD FOR ISENTROPIC COMPRESSIBLE FLOW ON PIPE NETWORKS

作者：Egger H^*

来源：SIAM Journal on Scientific Computing, 2018, 40(1): A108-A129.

DOI：10.1137/16M1094373

• compressible flow
• variational methods
• energy estimates
• Galerkin approximation
• mixed finite elements
• implicit time discretization

We consider the numerical approximation of compressible flow in a pipe network. Appropriate coupling conditions are formulated that allow us to derive a variational characterization of solutions and to prove global balance laws for the conservation of mass and energy on the whole network. This variational principle, which is the basis of our further investigations, is amenable to a conforming Galerkin approximation by mixed finite elements. The resulting semidiscrete problems are locally well-posed and automatically inherit the global conservation laws for mass and energy from the continuous level. We also consider the subsequent discretization in time by a problem adapted implicit time stepping scheme which leads to conservation of mass and a slight dissipation of energy of the full discretization. The well-posedness of the fully discrete scheme is analyzed, and a fixed-point iteration is proposed for the solution of the nonlinear systems arising in every single time step. Some computational results are presented for illustration of our theoretical findings and for demonstration of the robustness and accuracy of the new method.

• 出版日期2018