Search results for "High-order accuracy"
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HIGH-ORDER ACCURATE EMBEDDED-BOUNDARY DISCONTINUOUS GALERKIN METHODS FOR INVISCID GAS DYNAMICS
2022
This work presents a computational framework for solving the equations of inviscid gas dynamics over embedded geometries based on the discontinuous Galerkin (DG) method. The novelty of the framework is the ability to achieve high-order accuracy in the regions of smooth flow and to handle the presence of solution discontinuities via suitably introduced damping terms, which allow controlling spurious oscillations that are typical of high-order methods for first-order hyperbolic PDEs. The framework employs block structured Cartesian grids where a level set function defines implicitly the considered geometry. The domain is partitioned by intersecting the grid and the level set function, such th…
Modeling wave propagation in elastic solids via high-order accurate implicit-mesh discontinuous Galerkin methods
2022
A high-order accurate implicit-mesh discontinuous Galerkin framework for wave propagation in single-phase and bi-phase solids is presented. The framework belongs to the embedded-boundary techniques and its novelty regards the spatial discretization, which enables boundary and interface conditions to be enforced with high-order accuracy on curved embedded geometries. High-order accuracy is achieved via high-order quadrature rules for implicitly-defined domains and boundaries, whilst a cell-merging strategy addresses the presence of small cut cells. The framework is used to discretize the governing equations of elastodynamics, written using a first-order hyperbolic momentum-strain formulation…