On the development of an implicit high-order Discontinuous Galerkin method for DNS and implicit LES of turbulent flows

Bassi, Francesco; Botti, Lorenzo Alessio; Colombo, Alessandro; Crivellini, Andrea; Ghidoni, Antonio; Massa, Francesco Carlo

doi:10.1016/j.euromechflu.2015.08.010

Cited by 66 publications

(44 citation statements)

References 58 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The discontinuous Galerkin method was proposed in the seventies of the previous century in [42] and constant development of the method has been observed since the time, see [9,13,19,34,44] and its application to many problems, such as analysing plates and shell [17,36], elastic wave propagation [6,7] or fluid floats [3,32]. The present paper constitutes another step towards developing the DG method, with particular attention to the DGFD method.…”

Section: Introductionmentioning

confidence: 99%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

View full text Add to dashboard Cite

The paper deals with high-order discontinuous Galerkin (DG) method with the approximation order that exceeds 20 and reaches 100 and even 1000 with respect to one-dimensional case. To achieve such a high order solution, the DG method with finite difference method has to be applied. The basis functions of this method are high-order orthogonal Legendre or Chebyshev polynomials. These polynomials are defined in one-dimensional space (1D), but they can be easily adapted to two-dimensional space (2D) by cross products. There are no nodes in the elements and the degrees of freedom are coefficients of linear combination of basis functions. In this sort of analysis the reference elements are needed, so the transformations of the reference element into the real one are needed as well as the transformations connected with the mesh skeleton. Due to orthogonality of the basis functions, the obtained matrices are sparse even for finite elements with more than thousands degrees of freedom. In consequence, the truncation errors are limited and very high-order analysis can be performed. The paper is illustrated with a set of benchmark examples of 1D and 2D for the elliptic problems. The example presents the great effectiveness of the method that can shorten the length of calculation over hundreds times.

show abstract

Section: Introductionmentioning

confidence: 99%

Very high order discontinuous Galerkin method in elliptic problems

Jaśkowiec

2017

Comput Mech

View full text Add to dashboard Cite

show abstract

“…In recent years, due to the increasing computational power and accuracy requirement, Discontinuous Galerkin (DG) method has become one of the most promising approaches to highfidelity fluid dynamic computations in many technical areas, such as aeronautics, aeroacoustics and turbomachinery [17,3,2]. DG method proved to be very well suited for the Direct Numerical Simulation (DNS) [16,15,32] and the Large Eddy Simulation (LES) [31] of turbulent flows.…”

Section: Introductionmentioning

confidence: 99%

High-Order Linearly Implicit Two-Step Peer Methods for the Discontinuous Galerkin Solution of the Incompressible Rans Equations

Massa¹,

Noventa²,

Bassi³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

View full text Add to dashboard Cite

Abstract. In recent years the increasing attention to high-order Finite Volume (FV), Finite Element (FE) and spectral methods and the growth of computing power promote the development of high-order temporal schemes to perform robust, accurate and efficient unsteady long-time simulations. In this context, some features of the Discontinuous Galerkin finite element (DG) methods, e.g. compactness and flexibility, can be advantageous both for explicit and implicit time integration approaches. Explicit schemes can achieve very high accuracy, but are limited by time-step restrictions, while implicit schemes, even if memory consuming, can overcome time-step limitations, thus improving the time integration efficiency. During last decades several high order implicit temporal schemes have been developed, and some of them have been successfully coupled with DG methods. However these schemes can show the order reduction if applied to very stiff problems or problems with time-dependent boundary conditions. To overcome these limitations, high-order linearly implicit two-step peer methods have been proposed and successfully applied to the numerical solution of differential-algebraic equations. The aim of the present work is to implement high-order two-step peer methods in a DG code and assess their performance for the unsteady solution of the incompressible Navier-Stokes (INS) and Reynolds Averaged Navier-Stokes equations (RANS) equations.

show abstract

“…DG methods have been successfully applied to the simulation of turbulent flows by solving the Reynolds averaged Navier-Stokes (RANS) equations [1,2,3], and more recently, have also been found very well suited for the Direct Numerical Simulation (DNS) as well as Implicit Large Eddy Simulation (ILES) of turbulent flows [4,5] due to their favourable dispersion and dissipation properties. One of the advantages of DG methods is the use of a compact stencil, which is independent of the degree of polynomial approximation and is thus well suited for massively parallel implementations.…”

Section: Introductionmentioning

confidence: 99%

Hybrid Openmp/Mpi Parallelization of a High–order Discontinuous Galerkin CFD Solver

Bassi¹,

Colombo²,

Crivellini³

et al. 2016

Proceedings of the VII European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS Congress 2016)

View full text Add to dashboard Cite

Abstract. This paper describes the implementation of an hybrid OpenMP/MPI parallelization strategy in a Discontinuous Galerkin solver used for DNS and LES or CAA computations, to fruitfully exploit the modern massively parallel HPC facilities. It is usually believed that the sheared memory view of OpenMP can easily increase the parallel efficiency of codes dealing with multi-core clusters. The idea consists of running calculations on those machines restricting as much as possible the use of the MPI library to the communications between nodes and exploiting the shared memory paradigm within a node. However, in practice, the achievement of a real parallel performance gain is not straightforward. Moreover, as far as DG solvers are concerned, almost nothing is reported in the current literature about the hybrid MPI/OpenMP implementation. In this work a colouring algorithm has been employed for OpenMP. The resulting hybrid strategy performs quite satisfactory, since generally it is more efficient of the pure MPI implementation. However, the performances are heavily dependent on hardware platforms, as well as on computational details such as the polynomial order of space discretization or the number of computational elements. Several scalability tests have been performed, resulting in the conclusion that the best performance can be achieved only with a proper choice of the number of MPI partition and OpenMP threads to be used within a single node. The reliability of the method was here assessed by solving the Taylor Green vortex problem at Reynolds numbers equal to 800 and 1600 and the Linear Euler acustic scattering from a rigid sphere.

show abstract

On the development of an implicit high-order Discontinuous Galerkin method for DNS and implicit LES of turbulent flows

Cited by 66 publications

References 58 publications

Very high order discontinuous Galerkin method in elliptic problems

Very high order discontinuous Galerkin method in elliptic problems

High-Order Linearly Implicit Two-Step Peer Methods for the Discontinuous Galerkin Solution of the Incompressible Rans Equations

Hybrid Openmp/Mpi Parallelization of a High–order Discontinuous Galerkin CFD Solver

Contact Info

Product

Resources

About