High‐resolution p‐adaptive DG simulations of flows with moving shocks

Panourgias, Konstantinos; Papoutsakis, Andreas; Ekaterinaris, John A.

doi:10.1002/fld.3893

Cited by 11 publications

(8 citation statements)

References 39 publications

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“…Demonstration is performed first for one-and two-dimensional test problems with exact solutions these cases were computed with threedimensional meshes. For certain cases, the benefits that could be obtained from using p-type refinement 43 to better resolve complex flow structures are demonstrated. Furthermore, adaptive mesh refinement could be employed to achieve crisper resolution of moving discontinuities.…”

Section: Numerical Examplesmentioning

confidence: 98%

A dissipative Filter for the Discontinuous Galerkin method

Panourgias

Ekaterinaris²

2015

53rd AIAA Aerospace Sciences Meeting

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Complex three dimensional flows in domains with nontrivial geometry require use of mixed type unstructured meshes. The discontinuous Galerkin (DG) method is an unstructured grid method and development of a unified approach for discontinuity capturing with the DG method when higher order expansions are employed is therefore required. A systematic procedure for incorporating a dissipative mechanism to DG discretizations in unstructured meshes is developed. This adaptive non-linear dissipative mechanism enables capturing discontinuities and steep flow gradients without numerical oscillations. A filter designed and extensively used in the development of low dissipative well-balanced high order accurate finite difference schemes is employed. The filtering operator is adapted to the finite element context of DG discretizations. The filter operator is constructed and applied in the canonical computational domain where it can be applied in a direction per direction basis and then extended for all element types in unstructured meshes using collapsed coordinate transformations. The performance of the proposed dissipative mechanism is demonstrated and evaluated for different orders of expansions for one-dimensional and multidimensional problems with exact solutions. It is further applied for a number of standard inviscid flow test problems including strong shocks interactions to demonstrate the potential of the method. The dissipative mechanism yields results comparable to three-dimensional TVB and hierarchical limiting. Furthermore, the proposed approach is suitable for h/p-adaptivity in order to locally enhance resolution for three dimensional flow simulations that include discontinuities and complex flow features.

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Section: Numerical Examplesmentioning

confidence: 98%

A dissipative Filter for the Discontinuous Galerkin method

Panourgias

Ekaterinaris²

2015

53rd AIAA Aerospace Sciences Meeting

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“…Implementation of p‐refinement is performed in a parallel environment, and it is straightforward with the hierarchical Legendre polynomial bases; it is however more complicated for divergence‐free vector bases. Application of both h‐ and p‐adaptivity for the DG method requires information exchange only at the element faces and has been validated and demonstrated that it is conservative and for problems with smooth solutions converges to the design order of accuracy of the scheme . Numerical solutions with p‐adaptivity were also obtained for flows including discontinuities .…”

Section: P‐adaptivitymentioning

confidence: 99%

“…Application of both h-and p-adaptivity for the DG method requires information exchange only at the element faces and has been validated and demonstrated that it is conservative and for problems with smooth solutions converges to the design order of accuracy of the scheme. 52,53 Numerical solutions with p-adaptivity were also obtained for flows including discontinuities. 54 For large scale three-dimensional simulations, it is important to ensure that the parallel efficiency is high during the entire course of the computation.…”

Section: P-adaptivitymentioning

confidence: 99%

A p‐adaptive method for electromagnetic wave propagation

Panourgias

Ekaterinaris²

2017

Numerical Meth Engineering

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Summary The discontinuous Galerkin FEM is used for the numerical solution of the three‐dimensional Maxwell equations. Control of errors in the numerical level for the divergence‐free constraint of the magnetic field can be obtained through the use of divergence‐free vector bases. In this work, the so‐called perfectly hyperbolic formulation of the Maxwell equations is used to retain both divergence‐free magnetic field and in the presence of charges to satisfy the Gauss constraint for the electric field at the numerical level. For both approaches, it is found that higher‐order approximations have favorable effect on the preservation of the divergence constraints and that the perfectly hyperbolic formulations retains these errors to a lower level. It is shown that high‐order accuracy in space and time is achieved in unstructured meshes using implicit time marching. For nonuniform meshes, local resolution refinement is used using p‐type adaptivity to ensure accurate electromagnetic wave propagation. Thus, the potential of the method to reach the required higher resolution in anisotropic meshes and obtain accurate electromagnetic wave propagation with reduced computational effort is demonstrated.

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“…In compressible, dispersed, multiphase flows we observe the interaction of the macroscopic flow in the following ways: i) with refined structures due to compressibility (e.g. shock and acoustic waves [5,6], thermal effects and chemical reaction regions [7], [8], [9]), ii) with vortical structures [10], and iii) with dispersed micro-scale droplets and particles [11], moving walls and detailed solid structures [12] or solidification interfaces [13].…”

Section: Introductionmentioning

confidence: 99%

“…Firstly, this can be achieved by increasing the number of basis functions used for the discretisation of the field variables, resulting in an increase of the degrees of freedom within the element and the order of accuracy of the discretisation (i.e. p-type refinement) [15,16]. Secondly, this can be achieved by local increase of mesh resolution (i.e.…”

Section: Introductionmentioning

confidence: 99%

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

Papoutsakis

Sazhin

Begg

et al. 2018

Journal of Computational Physics

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We present an Adaptive Mesh Refinement (AMR) method suitable for hybrid unstructured meshes that allows for local refinement and de-refinement of the computational grid during the evolution of the flow. The adaptive implementation of the Discontinuous Galerkin (DG) method introduced in this work (ForestDG) is based on a topological representation of the computational mesh by a hierarchical structure consisting of oct-quad-and binary trees. Adaptive mesh refinement (h-refinement) enables us to increase the spatial resolution of the computational mesh in the vicinity of the points of interest such as interfaces, geometrical features, or flow discontinuities. The local increase in the expansion order (p-refinement) at areas of high strain rates or vorticity magnitude results in an increase of the order of accuracy in the region of shear layers and vortices. A graph of unitarian-trees, representing hexahedral, prismatic and tetrahedral elements is used for the representation of the initial domain. The ancestral elements of the mesh can be split into self-similar elements allowing each tree to grow branches to an arbitrary level of refinement. The connectivity of the elements, their genealogy and their partitioning are described by linked lists of pointers. An explicit calculation of these relations, presented in this paper, facilitates the on-the-fly splitting, merging and repartitioning of the computational mesh by rearranging the links of each node of the tree with a minimal computational overhead. The modal basis used in the DG implementation facilitates the mapping of the fluxes across the non conformal faces. The AMR methodology is presented and assessed using a series of inviscid and viscous test cases. Also, the AMR methodology is used for the modelling of the interaction between droplets and the carrier phase in a two-phase flow. This approach is applied to the analysis of a spray injected into a chamber of quiescent air, using the Eulerian-Lagrangian approach. This enables us to refine the computational mesh in the vicinity of the droplet parcels and accurately resolve the coupling between the two phases.

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High‐resolution p‐adaptive DG simulations of flows with moving shocks

Cited by 11 publications

References 39 publications

A dissipative Filter for the Discontinuous Galerkin method

A dissipative Filter for the Discontinuous Galerkin method

A p‐adaptive method for electromagnetic wave propagation

An efficient Adaptive Mesh Refinement (AMR) algorithm for the Discontinuous Galerkin method: Applications for the computation of compressible two-phase flows

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