Optimized explicit Runge-Kutta schemes for the spectral difference method applied to wave propagation problems

Explicit Runge-Kutta schemes with large stable step sizes are developed for integration of high order spectral difference spatial discretization on quadrilateral grids. The new schemes permit an effective time step that is substantially larger than the maximum admissible time step of standard explicit Runge-Kutta schemes available in literature. Furthermore, they have a small principal error norm and admit a low-storage implementation. The advantages of the new schemes are demonstrated through application to the Euler equations and the linearized Euler equations.Comment: 37 pages, 3 pages of appendi

Construction of Modern Robust Nodal Discontinuous Galerkin Spectral Element Methods for the Compressible Navier-Stokes Equations

Discontinuous Galerkin (DG) methods have a long history in computational physics and engineering to approximate solutions of partial differential equations due to their high-order accuracy and geometric flexibility. However, DG is not perfect and there remain some issues. Concerning robustness, DG has undergone an extensive transformation over the past seven years into its modern form that provides statements on solution boundedness for linear and nonlinear problems. This chapter takes a constructive approach to introduce a modern incarnation of the DG spectral element method for the compressible Navier-Stokes equations in a three-dimensional curvilinear context. The groundwork of the numerical scheme comes from classic principles of spectral methods including polynomial approximations and Gauss-type quadratures. We identify aliasing as one underlying cause of the robustness issues for classical DG spectral methods. Removing said aliasing errors requires a particular differentiation matrix and careful discretization of the advective flux terms in the governing equations.Comment: 85 pages, 2 figures, book chapte

Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas

Data for "Fully Implicit Time Stepping can be Efficient on Parallel Computers"

Benchmark data and python plotting program

Maximum-principle-satisfying space-time conservation element and solution element scheme applied to compressible multifluids

2016-2017 > Academic research: refereed > Publication in refereed journal201804_a bcmaAccepted ManuscriptOthersState Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology; Army Research Office (ARO)Publishe

Evaluation of next generation of high-order compressible fluid dynamic solvers on the cloud computing for complex industrial flows

Industrially relevant computational fluid dynamics simulations frequently require vast computational resources that are only available to governments, wealthy corporations, and wealthy institutions. Thus, in many contexts and realities, high-performance computing grids and cloud resources on demand should be evaluated as viable alternatives to conventional computing clusters. In this work, we present the analysis of the time-to-solution and cost of an entropy stable collocated discontinuous Galerkin (SSDC) compressible computational fluid dynamics framework on Ibex, the on-premises cluster at KAUST, and the Amazon Web Services Elastic Compute Cloud for complex compressible flows. SSDC is a prototype of the next generation computational fluid dynamics frameworks developed following the road map established by the NASA CFD vision 2030. We simulate complex flow problems using high-order accurate fully-discrete entropy stable algorithms. In terms of time-to-solution, the Amazon Elastic Compute Cloud delivers the best performance, with the Graviton2 processors based on the Arm architecture being the fastest. However, the results also indicate that the Ibex nodes based on the AMD Rome architecture deliver good performance, close to those observed for the Amazon Elastic Compute Cloud. Furthermore, we observed that computations performed on the Ibex on-premises cluster are currently less expensive than those performed in the cloud. Our findings could be used to develop guidelines for selecting high-performance computing cloud resources to simulate realistic fluid flow problems