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A variational approach to high-order r-adaptation
A variational framework, initially developed for high-order mesh optimis...
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Dynamical p-adaptivity for LES of compressible flows in a high order DG framework
We investigate the possibility of reducing the computational burden of L...
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Naturally curved quadrilateral mesh generation using an adaptive spectral element solver
We describe an adaptive version of a method for generating valid natural...
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High-order curvilinear hybrid mesh generation for CFD simulations
We describe a semi-structured method for the generation of high-order hy...
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Truncation Error Estimation in the p-Anisotropic Discontinuous Galerkin Spectral Element Method
In the context of Discontinuous Galerkin Spectral Element Methods (DGSEM...
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hr-adaptivity for nonconforming high-order meshes with the target matrix optimization paradigm
We present an hr-adaptivity framework for optimization of high-order mes...
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Industry-Relevant Implicit Large-Eddy Simulation of a High-Performance Road Car via Spectral/hp Element Methods
We present a successful deployment of high-fidelity Large-Eddy Simulatio...
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rp-adaptation for compressible flows
We present an rp-adaptation strategy for the high-fidelity simulation of compressible inviscid flows with shocks. The mesh resolution in regions of flow discontinuities is increased by using a variational optimiser 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. 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 at transonic and supersonic flow regimes. The method was implemented in the open-source spectral/hp element framework Nektar++, and 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 accuracy.
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