rp‐adaptation for compressible flows
Copyright policy )rp‐adaptation for compressible flows
AbstractWe present a novel rp‐adaptation strategy for high‐fidelity simulations of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimizer to r‐adapt the mesh and cluster degrees of freedom there. In regions of smooth flow, we locally increase or decrease the local resolution through increasing or decreasing the polynomial order of the elements, respectively. This dual approach allows us to take advantage of the strengths of both methods for best computational performance, thereby reducing the overall cost of the simulation. The adaptation workflow uses a sensor for both discontinuities and smooth regions that is cheap to calculate, but the framework is general and could be used in conjunction with other feature‐based sensors or error estimators. We demonstrate this proof‐of‐concept using two geometries in transonic and supersonic flow regimes. The method has been implemented in the open‐source spectral/hp element framework Nektar++, and adaptivity is performed by its dedicated high‐order mesh generation tool NekMesh. The results show that the proposed rp‐adaptation methodology is a reasonably cost‐effective way of improving simulation accuracy.
- Imperial College London United Kingdom
- University of Exeter United Kingdom
FOS: Computer and information sciences, Technology, J.2, G.1.8, 76N15 (Secondary), adaptivity, Computational Engineering, Finance, and Science (cs.CE), Error estimation, Engineering, Discontinuous Galerkin, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, Interdisciplinary Applications, Computer Science - Computational Engineering, Finance, and Science, compressible flow, 65M50, Fluids, cs.CE, Multidisciplinary, Compressible flow, 65N30, I.3.5, Physics - Fluid Dynamics, Numerical Analysis (math.NA), 76H05, Computational Physics (physics.comp-ph), DISCONTINUOUS GALERKIN METHOD, 004, cs.CG, Adaptivity, Error bounds for initial value and initial-boundary value problems involving PDEs, Euler flow, 65N50 (Primary) 35Q31, Physical Sciences, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Compressible fluids and gas dynamics, fluids, Physics - Computational Physics, 35Q35, 65M60, G.4, Computational Geometry (cs.CG), math.NA, FOS: Physical sciences, 65N50 (Primary) 35Q31, 35Q35, 65M50, 65M60, 65N30, 76H05, 76J20, 76N15 (Secondary), FOS: Mathematics, Mathematics - Numerical Analysis, cs.NA, Science & Technology, I.6.3, Fluid Dynamics (physics.flu-dyn), 76J20, 620, physics.flu-dyn, physics.comp-ph, error estimation, Computer Science - Computational Geometry, I.6.6, G.1.8; G.4; I.3.5; I.6.3; I.6.6; J.2, Mathematics, Finite element methods applied to problems in fluid mechanics, discontinuous Galerkin
FOS: Computer and information sciences, Technology, J.2, G.1.8, 76N15 (Secondary), adaptivity, Computational Engineering, Finance, and Science (cs.CE), Error estimation, Engineering, Discontinuous Galerkin, Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs, Interdisciplinary Applications, Computer Science - Computational Engineering, Finance, and Science, compressible flow, 65M50, Fluids, cs.CE, Multidisciplinary, Compressible flow, 65N30, I.3.5, Physics - Fluid Dynamics, Numerical Analysis (math.NA), 76H05, Computational Physics (physics.comp-ph), DISCONTINUOUS GALERKIN METHOD, 004, cs.CG, Adaptivity, Error bounds for initial value and initial-boundary value problems involving PDEs, Euler flow, 65N50 (Primary) 35Q31, Physical Sciences, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Compressible fluids and gas dynamics, fluids, Physics - Computational Physics, 35Q35, 65M60, G.4, Computational Geometry (cs.CG), math.NA, FOS: Physical sciences, 65N50 (Primary) 35Q31, 35Q35, 65M50, 65M60, 65N30, 76H05, 76J20, 76N15 (Secondary), FOS: Mathematics, Mathematics - Numerical Analysis, cs.NA, Science & Technology, I.6.3, Fluid Dynamics (physics.flu-dyn), 76J20, 620, physics.flu-dyn, physics.comp-ph, error estimation, Computer Science - Computational Geometry, I.6.6, G.1.8; G.4; I.3.5; I.6.3; I.6.6; J.2, Mathematics, Finite element methods applied to problems in fluid mechanics, discontinuous Galerkin
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