Browsing by Author "Yuan, Dean"
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Item Open Access Hybrid discontinuous Galerkin-finite volume techniques for compressible flows on unstructured meshes(Elsevier, 2022-11-11) Maltsev, Vadim; Yuan, Dean; Jenkins, Karl W.; Skote, Martin; Tsoutsanis, PanagiotisIn this paper we develop a family of arbitrarily high-order non-oscillatory hybrid Discontinuous Galerkin(DG)-Finite Volume(FV) schemes for mixed-element unstructured meshes. Their key ingredient is a switch between a DG method and a FV method based on the CWENOZ scheme when invalid solutions are detected by a troubled cell indicator checking the unlimited DG solution. Therefore, the high order of accuracy offered by DG is preserved in smooth regions of the computational domain, while the robustness of FV is utilized in regions with strong gradients. The high-order CWENOZ variant used has the same spatial order of accuracy as the DG variant, while representing one of the most compact applications on unstructured meshes, therefore simplifying the implementation, reducing the computational overhead associated with large stencils of the original WENO reconstruction without sacrificing the desirable non-oscillatory properties of the schemes. We carefully investigate several parameters associated with the switching between DG and FV methods including the troubled cell indicators in a priori fashion. For the first time in the literature, we investigate the definition of the bounds for an admissible solution, the frequency by which we use the troubled cell indicators, and the evolution of the percentage of troubled cells for unsteady test problems. The 2D and 3D Euler equations are solved for well established test problems and compared with computational or experimental reference solutions. All the methods have been implemented and deployed within the UCNS3D open-source high-order unstructured Computational Fluid Dynamics (CFD) solver. The present coupling has the potential to improve the shortcomings of both FV-DG in a computational efficient manner. The improved accuracy and robustness provided is a characteristic of paramount importance for industrial-scale CFD applications, and favours the extension to other systems of governing equations.Item Open Access Numerical investigation of the inviscid Taylor-Green Vortex using an adaptive filtering method for a modal Discontinuous Galerkin method(Taylor and Francis, 2024-04-28) Yuan, Dean; Jenkins, Karl W.; Tsoutsanis, PanagiotisImplicit Large Eddy Simulation and under-resolved Direct Numerical Simulation bypass the complexity and uncertainty of turbulence modelling by using the numerical dissipation of the scheme as a subgrid scale model. High-order methods allow for more accurate capturing of smaller scale structures but suffer from energy pile-up in the higher modes which leads to instability in under-resolved applications. This work presents a filtered modal Discontinuous Galerkin method which adaptively determines the filter strength, avoiding unnecessary degradation of accuracy while maintaining stability. The method is applied to the inviscid Taylor-Green Vortex, a challenging test case which exhibits under-resolved turbulence for which few published results exist. This goal of this work is to present the adaptive filtering method which achieves robustness and accuracy despite a low number of degrees of freedom, as well as to publish a quantity of relevant data for the inviscid TGV problem.Item Open Access Numerical simulation of the inviscid Taylor-Green Vortex using a Discontinuous Galerkin method with adaptive filtering to stabilize the solution: data(Cranfield University, 2024-03-07 08:39) Yuan, DeanNumerical simulation of the inviscid Taylor-Green Vortex using a Discontinuous Galerkin method with adaptive filtering to stabilize the solution.