1,225 research outputs found
A matrix-free high-order discontinuous Galerkin compressible Navier-Stokes solver: A performance comparison of compressible and incompressible formulations for turbulent incompressible flows
Both compressible and incompressible Navier-Stokes solvers can be used and
are used to solve incompressible turbulent flow problems. In the compressible
case, the Mach number is then considered as a solver parameter that is set to a
small value, , in order to mimic incompressible flows.
This strategy is widely used for high-order discontinuous Galerkin
discretizations of the compressible Navier-Stokes equations. The present work
raises the question regarding the computational efficiency of compressible DG
solvers as compared to a genuinely incompressible formulation. Our
contributions to the state-of-the-art are twofold: Firstly, we present a
high-performance discontinuous Galerkin solver for the compressible
Navier-Stokes equations based on a highly efficient matrix-free implementation
that targets modern cache-based multicore architectures. The performance
results presented in this work focus on the node-level performance and our
results suggest that there is great potential for further performance
improvements for current state-of-the-art discontinuous Galerkin
implementations of the compressible Navier-Stokes equations. Secondly, this
compressible Navier-Stokes solver is put into perspective by comparing it to an
incompressible DG solver that uses the same matrix-free implementation. We
discuss algorithmic differences between both solution strategies and present an
in-depth numerical investigation of the performance. The considered benchmark
test cases are the three-dimensional Taylor-Green vortex problem as a
representative of transitional flows and the turbulent channel flow problem as
a representative of wall-bounded turbulent flows
Second-order accurate genuine BGK schemes for the ultra-relativistic flow simulations
This paper presents second-order accurate genuine BGK (Bhatnagar-Gross-Krook)
schemes in the framework of finite volume method for the ultra-relativistic
flows. Different from the existing kinetic flux-vector splitting (KFVS) or
BGK-type schemes for the ultra-relativistic Euler equations, the present
genuine BGK schemes are derived from the analytical solution of the
Anderson-Witting model, which is given for the first time and includes the
"genuine" particle collisions in the gas transport process. The BGK schemes for
the ultra-relativistic viscous flows are also developed and two examples of
ultra-relativistic viscous flow are designed. Several 1D and 2D numerical
experiments are conducted to demonstrate that the proposed BGK schemes not only
are accurate and stable in simulating ultra-relativistic inviscid and viscous
flows, but also have higher resolution at the contact discontinuity than the
KFVS or BGK-type schemes.Comment: 41 pages, 13 figure
- …