Bulletin of the American Physical Society
72nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 64, Number 13
Saturday–Tuesday, November 23–26, 2019; Seattle, Washington
Session L41: CFD: Discontinuous Galerkin Methods |
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Chair: Eric Johnsen, University of Michigan Room: 6c |
Monday, November 25, 2019 1:45PM - 1:58PM |
L41.00001: High-order extended discontinuous Galerkin methods for sharp shock-capturing? Martin Oberlack, Markus Geisenhofer, Florian Kummer, Bjoern Mueller We study unsteady high Mach number flows using a Discontinuous Galerkin (DG) solver (Mueller 2016) that was extended to immersed boundary methods (IBM) using level sets. Cell-agglomeration was applied for small and ill-shaped cut cells. To cope with shocks, we used an artificial viscosity shock-capturing approach (Persson 2006) that was coupled to IBM (Geisenhofer 2019). There a shock sensor is used to identify critical cells and artificial viscosity smoothens the solution. The severe time stepping restrictions due to an explicit time step together with the additional diffusive term are dealt by an adaptive local time stepping (LTS) approach (Winters 2014) that dynamically (re-)partitions the grid according to their local time step. Presently we extend the shock-fitting techniques using an eXtended DG (XDG) method (Kummer 2016) to regain the desirable DG convergence rates and a sharp jump representation. For this, we first investigate shock tracking in 1D, where we prescribe the flow properties across shocks using the Rankine-Hugoniot conditions in combination with the level set propagation speed. Second, we consider the formation of stationary shocks in 2D, where the artificial viscosity IBM, LTS method will be the initial solution to be morphed to a XDG shock-fitting approach. [Preview Abstract] |
Monday, November 25, 2019 1:58PM - 2:11PM |
L41.00002: Reacting flow simulations using high-order discontinuous Galerkin methods Kihiro Bando, Matthias Ihme, Michael Sekachev High-order discontinuous Galerkin (DG) methods have been an increasingly popular topic of research for enabling high-fidelity simulations on complex geometries. They present several attractive features such as high-order accuracy on arbitrary mesh topologies, compact implementation and support of advanced $hp$-refinement strategies which can be leveraged to increase computational efficiency. However, the application of such methods to flows presenting complex thermodynamics and chemical reactions is still sparse. In particular, the accurate prediction of such flows requires the consideration of complex transport and the treatment of stiff reaction chemistry. This talk will discuss challenges associated with reacting flow simulations in the context of a DG discretization. Simple one-dimensional cases will first be investigated to gain insight at the fundamental properties of the scheme when applied to such flows. Subsequently, more challenging cases in multiple dimensions will be examined to highlight the performance as well as the need for further developments to enable reacting flow simulations using DG methods. [Preview Abstract] |
Monday, November 25, 2019 2:11PM - 2:24PM |
L41.00003: Development of a Four-Way-Coupled Lagrangian Particle Method for Discontinuous Galerkin Schemes Eric Ching, Matthias Ihme In this talk, we present an Euler-Lagrange methodology within the framework of discontinuous Galerkin methods. We discuss strategies to track particle trajectories through curved elements near walls while taking into account finite particle sizes. The back-coupling of particles to the carrier gas is treated in an efficient manner. In addition, we introduce a particle-particle collision algorithm that utilizes information provided by the geometric mapping from physical space to reference space. In doing so, the proposed algorithm reduces the number of particle pair inspections compared to standard methods. The algorithm is verified by drawing comparisons to kinetic theory. To demonstrate the capability of the multiphase flow solver, we consider a variety of test cases that include hypersonic dusty flows over blunt bodies and erosive action of sand blasting. [Preview Abstract] |
Monday, November 25, 2019 2:24PM - 2:37PM |
L41.00004: An Enriched-Basis Discontinuous Galerkin Method for Wall-Modeled Large-Eddy Simulations Steven R. Brill, Matthias Ihme We developed an enriched-basis discontinuous Galerkin (DG) method for wall-modeled large-eddy simulations (WMLES) of turbulent flows. Ordinarily, higher-order methods, such as DG-schemes, require significant mesh refinement near the wall in order to resolve the turbulent boundary layer without spurious oscillations due to large gradients in the boundary layer. To avoid this issue, we enrich the traditional polynomial basis with a problem-specific non-polynomial basis function in the near-wall elements in order to capture the inner boundary-layer structure while still using a coarse mesh. In this method, the enrichment function is not required to be active, but is chosen by the Galerkin procedure when it is optimal, such as near the wall. As a result, the enrichment basis functions capture the mean behavior near the wall, the polynomial basis functions resolve the large eddies, and a subgrid scale model represents the small scale behavior. We discuss the procedure for choosing the proper enrichment functions for a problem and integrating non-polynomial basis functions into the DG framework. The method is demonstrated in application to turbulent channel flows and other canonical wall-bounded turbulent flows. [Preview Abstract] |
Monday, November 25, 2019 2:37PM - 2:50PM |
L41.00005: A High-Order Lagrangian Discontinuous Galerkin Method on Hybrid Curved Meshes xiaodong liu, Nathaniel Morgan, Donald Burton We present a high-order (up to fourth order) Lagrangian DG hydrodynamic method using subcell mesh stabilization (SMS) for compressible flows on hybrid curved meshes (up to cubic meshes) in 2D Cartesian coordinates. The physical evolution equations for the specific volume, velocity, and specific total energy are discretized using a modal DG method . The challenge for Lagrangian hydrodynamics is to guarantee the stable mesh motion for the edge vertex, that can easily deform in unphysical ways. With SMS, each cell is decomposed into several subcells, that move in a Lagrangian manner. The edge vertex is surrounded by several subcells so that enough information can be obtained, that is similar to the corner vertex. As such, the same multidirectional approximate Riemann problem can be solved for these both types of vertices. This SMS scheme enables stable mesh motion and accurate solutions in a context of the Lagrangian high-order DG method. We also present effective limiting strategies that ensure monotonicity of the primitive variables with the high-order DG method. A suite of test problems are calculated to demonstrate the designed order of accuracy of this method and the robustness for the strong shock problems. [Preview Abstract] |
Monday, November 25, 2019 2:50PM - 3:03PM |
L41.00006: A Recovery-Assisted Discontinuous Galerkin Method for the Compressible Navier-Stokes Equations Eric Johnsen, Philip E. Johnson The Discontinuous Galerkin (DG) method is a promising approach for high-fidelity simulations of turbulent flows in complex geometries, given the method's capability for arbitrarily high orders of accuracy on unstructured meshes. We propose a DG approach for advection-diffusion equations (such as the Navier-Stokes equations) based on the principle of Recovery, whereby the underlying solution between two adjacent computational elements is "recovered" into a smooth, more accurate polynomial representation. By combining a biased approach to Recovery for advection with a compact gradient recovery for diffusion, we achieve $2p+2$ order of accuracy in the cell-average error on a nearest-neighbors stencil, where $p$ is the degree of the polynomial basis, and demonstrate higher efficiency than other state-of-the-art DG approaches. Several test cases, including compressible turbulence, are presented to support our method. [Preview Abstract] |
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