High order discontinuous Galerkin discretizations with a new limiting approach and positivity preservation for strong moving shocks

Kontzialis, Konstantinos; Ekaterinaris, John A.

doi:10.1016/j.compfluid.2012.10.009

Cited by 20 publications

(14 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recently, based on certain Gauss-Lobatto quadratures and positivity-preserving flux, Zhang and Shu [13][14][15] used Lax-Friedrichs flux and successfully developed a positivity-preserving approach for high-order discontinuous Galerkin methods. Such an approach is also applied to unstructured meshes and p-adaptive numerical solutions by Kontzialis and Ekaterinaris [18]. In a recent paper of Wang et al [16], they simplified the method and extended it to solve gaseous detonations.…”

Section: Introductionmentioning

confidence: 99%

Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock

Liu

Qiu

Goman

et al. 2016

Numer. Math. Theory Methods Appl.

View full text Add to dashboard Cite

Abstract. In order to suppress the failure of preserving positivity of density or pressure, a positivity-preserving limiter technique coupled with h-adaptive Runge-Kutta discontinuous Galerkin (RKDG) method is developed in this paper. Such a method is implemented to simulate flows with the large Mach number, strong shock/obstacle interactions and shock diffractions. The Cartesian grid with ghost cell immersed boundary method for arbitrarily complex geometries is also presented. This approach directly uses the cell solution polynomial of DG finite element space as the interpolation formula. The method is validated by the well documented test examples involving unsteady compressible flows through complex bodies over a large Mach numbers. The numerical results demonstrate the robustness and the versatility of the proposed approach.

show abstract

Section: Introductionmentioning

confidence: 99%

Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock

Liu

Qiu

Goman

et al. 2016

Numer. Math. Theory Methods Appl.

View full text Add to dashboard Cite

show abstract

“…On the other hand, implicit time marching for the P2 computation was necessary in order to overcome stability limitations imposed by the increase of the polynomial order expansion. For P2 or higher order accuracy, elements that were flagged for limiting according to the modified TVB limiter of Equation were set as P1, and the accuracy was increased away from them as it is shown in References . Because of high mesh resolution, there are no noticeable differences between P1 and P2 computations on the pressure contours (Figure (b) and (d) and Figure (b) and (d)).…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The basic limiter of Equation was used and also applied in a direction to direction basis in the canonical computational domain (Figure (a)) for the standard square elements in two dimensions and the standard cubic elements in three dimensions, rather than the physical space arbitrary elements. After limiting the characteristic variables in the computational domain, the conservative variables are formed and transferred back to the physical space.…”

Section: Discontinuous Galerkin Formulation For the Navier–stokes Equmentioning

confidence: 99%

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

Panourgias

Papoutsakis

Ekaterinaris

2014

Numerical Methods in Fluids

Self Cite

View full text Add to dashboard Cite

SUMMARYHigh‐order accurate DG discretization is employed for Reynolds‐averaged Navier–Stokes equations modeling of complex shock‐dominated, unsteady flow generated by gas issuing from a shock tube nozzle. The DG finite element discretization framework is used for both the flow field and turbulence transport. Turbulent flow in the near wall regions and the flow field is modeled by the Spalart–Allmaras one‐equation model. The effect of rotation on turbulence modeling for shock‐dominated supersonic flows is considered for accurate resolution of the large coherent and vortical structures that are of interest in high‐speed combustion and supersonic flows. Implicit time marching methodologies are used to enable large time steps by avoiding the severe time step limitations imposed by the higher order DG discretizations and the source terms. Sufficiently high mesh density is used to enable crisp capturing of discontinuities. A p − type refinement procedure is employed to accurately represent the vortical structures generated during the development of the flow. The computed solutions showed qualitative agreement with experiments. Copyright © 2014 John Wiley & Sons, Ltd.

show abstract

“…These higher order numerical solutions were the same as the second order numerical solution mainly because the TVB limiter was activated at many discontinuities and the accuracy dropped to piecewise linear expansion when the limiter is activated. 42 …”

Section: B Brio and Wu Shock Tube Problemmentioning

confidence: 97%

Numerical solution of ionized gas compressible flows under the influence of electromagnetic fields

Panourgias

Ekaterinaris

2013

21st AIAA Computational Fluid Dynamics Conference

Self Cite

View full text Add to dashboard Cite

The compressible Navier-Stokes equations are coupled with the full Maxwell equations and the resulting system of equations describing the flow of ionized gases under the influence of electromagnetic fields is solved numerically. The discontinuous Galerkin finite element method is used for the numerical solution. High order expansions for arbitrary-type elements are employed using orthogonal and hierarchical polynomial bases for the approximation of the solution in each element. For the Maxwell equations DG discretization is performed using divergence free vector bases for the magnetic field in order to preserve zero divergence in the element and retain the global implicit constraint of a divergence free magnetic field vector down to very low levels and up to the error caused by jumps at the element interfaces. Upwind fluxes of consistent Riemann solvers are used on the elements interfaces for both the flow and the electromagnetic fluxes. In order to avoid severe time step limitations imposed by the speed of light for the Maxwell system implicit time marching is used for the full system with high order implicit Rugne-Kutta methods. It is was found that the coupled system of the Navier-Stokes and the Maxwell equations must be advance in time simultaneously to avoid wrong wave shapes and propagation speeds that are obtained when the coupling source terms are lagged in time. A fully parallelized Jacobian free Newton Krylov iterative procedure is employed with the implicit solver. Computed solutions for classical MHD problems demonstrated good agreement with existing numerical results and exact solutions. However, the present coupling approach is more general than the MHD approximation and is demonstrated for cases where the time variation of the electric field is not negligible and the MHD approximation is not valid. I. IntroductionPlasma is referred to as the fourth state of matter. It is an ionized gas, often at high temperature, that consists of reactive particles such as electrons, ions, and radicals. Plasma in natural state is uncommon on earth but it is created in nature (lightning), it is produced in the laboratory, in devices, and industrial processes. In space however, more than 99% of all matter is in the plasma state, therefore, significant effort was devoted to MHD research in the past. Plasmas are categorized as thermal and non-thermal plasmas. In thermal plasmas the electrons and other species (atoms, ions) obtain thermal equilibrium. For non-thermal plasmas there is a difference in temperature of electrons and other species. In certain applications, for example in combustion and flow control, non-thermal plasmas could have an advantage over thermal plasmas because they are capable of depositing energy only in the active plasma species relevant to the flame ignition and/or flow stabilization.

show abstract

High order discontinuous Galerkin discretizations with a new limiting approach and positivity preservation for strong moving shocks

Cited by 20 publications

References 23 publications

Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock

Positivity-Preserving Runge-Kutta Discontinuous Galerkin Method on Adaptive Cartesian Grid for Strong Moving Shock

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

Numerical solution of ionized gas compressible flows under the influence of electromagnetic fields

Contact Info

Product

Resources

About