High Order Accurate Direct Arbitrary-Lagrangian-Eulerian ADER-MOOD Finite Volume Schemes for Non-Conservative Hyperbolic Systems with Stiff Source Terms (Communications in Computational Physics, 2018)
In this paper we present a 2D/3D high order accurate finite volume schemein the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolicsystems of partial differential equations with non-conservative products and stiffsource terms. This scheme is constructed with a single stencil polynomial reconstructionoperator, a one-step space-time ADER integration which is suitably designed fordealing even with stiff sources, a nodal solver with relaxation to determine the meshmotion, a path-conservative integration technique for the treatment of non-conservativeproducts and an a posteriori stabilization procedure derived from the so-called MultidimensionalOptimal Order Detection (MOOD) paradigm. In this work we considerthe seven equation Baer-Nunziato model of compressible multi-phase flows as a representativemodel involving non-conservative products as well as relaxation sourceterms which are allowed to become stiff. The new scheme is validated against a setof test cases on 2D/3D unstructured moving meshes on parallel machines and thehigh order of accuracy achieved by the method is demonstrated by performing a numericalconvergence study. Classical Riemann problems and explosion problems withexact solutions are simulated in 2D and 3D. The overall numerical code is also profiledto provide an estimate of the computational cost required by each component of thewhole algorithm.