scholarly journals High-order semi-Lagrangian kinetic scheme for compressible turbulence

2021 ◽  
Vol 104 (2) ◽  
Author(s):  
Dominik Wilde ◽  
Andreas Krämer ◽  
Dirk Reith ◽  
Holger Foysi
Keyword(s):  
Kinetic Scheme ◽  
High Order ◽  
Compressible Turbulence

scholarly journals Comparative Study of Three High Order Schemes for LES of Temporally Evolving Mixing Layers

2012 ◽  
Vol 12 (5) ◽  
pp. 1603-1622 ◽  
Author(s):  
Helen C. Yee ◽  
Bjorn Sjögreen ◽  
Abdellah Hadjadj
Keyword(s):  
High Order ◽  
Mixing Layers ◽  
Compressible Turbulence ◽  
Filter Method ◽  
Eighth Order ◽  
Base Scheme ◽  
High Order Schemes ◽  
Supersonic Regime ◽  
Seventh Order ◽  
Fifth Order

AbstractThree high order shock-capturing schemes are compared for large eddy simulations (LES) of temporally evolving mixing layers for different convective Mach numbers ranging from the quasi-incompressible regime to highly compressible supersonic regime. The considered high order schemes are fifth-order WENO (WENO5), seventh-order WENO (WENO7) and the associated eighth-order central spatial base scheme with the dissipative portion of WENO7 as a nonlinear post-processing filter step (WENO7fi). This high order nonlinear filter method of Yee & Sjögreen is designed for accurate and efficient simulations of shock-free compressible turbulence, turbulence with shocklets and turbulence with strong shocks with minimum tuning of scheme parameters. The LES results by WENO7fi using the same scheme parameter agree well with experimental results compiled by Barone et al., and published direct numerical simulations (DNS) work of Rogers & Moser and Pantano & Sarkar, whereas results by WENO5 and WENO7 compare poorly with experimental data and DNS computations.

A High-Order Accurate Gas-Kinetic Scheme for One- and Two-Dimensional Flow Simulation

2014 ◽  
Vol 15 (4) ◽  
pp. 911-943 ◽  
Author(s):  
Na Liu ◽  
Huazhong Tang
Keyword(s):  
Velocity Distribution ◽  
Particle Velocity ◽  
Fourth Order ◽  
Velocity Distribution Function ◽  
Kinetic Scheme ◽  
High Order ◽  
Third Order ◽  
Quartic Polynomial ◽  
Two Dimensional Flow ◽  
Cell Interface

AbstractThis paper develops a high-order accurate gas-kinetic scheme in the framework of the finite volume method for the one- and two-dimensional flow simulations, which is an extension of the third-order accurate gas-kinetic scheme [Q.B. Li, K. Xu, and S. Fu, J. Comput. Phys., 229(2010), 6715-6731] and the second-order accurate gas-kinetic scheme [K. Xu, J. Comput. Phys., 171(2001), 289-335]. It is formed by two parts: quartic polynomial reconstruction of the macroscopic variables and fourth-order accurate flux evolution. The first part reconstructs a piecewise cell-center based quartic polynomial and a cell-vertex based quartic polynomial according to the “initial” cell average approximation of macroscopic variables to recover locally the non-equilibrium and equilibrium single particle velocity distribution functions around the cell interface. It is in view of the fact that all macroscopic variables become moments of a single particle velocity distribution function in the gas-kinetic theory. The generalized moment limiter is employed there to suppress the possible numerical oscillation. In the second part, the macroscopic flux at the cell interface is evolved in fourth-order accuracy by means of the simple particle transport mechanism in the microscopic level, i.e. free transport and the Bhatnagar-Gross-Krook (BGK) collisions. In other words, the fourth-order flux evolution is based on the solution (i.e. the particle velocity distribution function) of the BGK model for the Boltzmann equation. Several 1D and 2D test problems are numerically solved by using the proposed high-order accurate gas-kinetic scheme. By comparing with the exact solutions or the numerical solutions obtained the second-order or third-order accurate gas-kinetic scheme, the computations demonstrate that our scheme is effective and accurate for simulating invisid and viscous fluid flows, and the accuracy of the high-order GKS depends on the choice of the (numerical) collision time.

Aeroacoustic Predictions Using High-Order Shock-Capturing Schemes

2003 ◽  
Vol 2 (2) ◽  
pp. 175-192 ◽  
Author(s):  
John A. Ekaterinaris
Keyword(s):  
Numerical Solutions ◽  
Sound Propagation ◽  
Finite Difference Methods ◽  
High Order ◽  
Curvilinear Coordinates ◽  
Compressible Turbulence ◽  
Test Problems ◽  
Complex Flows ◽  
Time Marching ◽  
Implicit And Explicit

High-order accurate, finite-difference methods, such as the compact centered schemes with spectral-type or characteristic-based filters and the weighted essentially non-oscillatory (WENO) schemes, which are used in high resolution CFD solutions and for DNS or LES of compressible turbulence, are applied to aeroacoustics. Implicit and explicit schemes are used for time marching. The accuracy of the numerical solutions is evaluated for test problems. It is found that these methods are appropriate for sound propagation in complex flows that require use of curvilinear coordinates. Therefore they are applicable for the prediction of sound generation from both smooth subsonic flows, and transonic or supersonic flows with discontinuities.

A parallel high-order compressible flows solver with domain decomposition method in the generalized curvilinear coordinates system

2019 ◽  
Vol 30 (1) ◽  
pp. 2-38 ◽  
Author(s):  
Arthur Piquet ◽  
Boubakr Zebiri ◽  
Abdellah Hadjadj ◽  
Mostafa Safdari Shadloo
Keyword(s):  
Domain Decomposition ◽  
Decomposition Method ◽  
Compressible Flows ◽  
Domain Decomposition Method ◽  
High Order ◽  
Curvilinear Coordinates ◽  
Compressible Turbulence ◽  
Complex Geometries ◽  
Content Type ◽  
Pipe Flows

Purpose This paper aims to present the development of a highly parallel finite-difference computational fluid dynamics code in generalized curvilinear coordinates system. The objectives are to handle internal and external flows in fairly complex geometries including shock waves, compressible turbulence and heat transfer. Design/methodology/approach The code is equipped with high-order discretization schemes to improve the computational accuracy of the solution algorithm. Besides, a new method to deal with the geometrical singularities, so-called domain decomposition method (DDM), is implemented. The DDM consists of using two different meshes communicating with each other, where the base mesh is Cartesian and the overlapped one a hollow cylinder. Findings The robustness of the present implemented code is appraised through several numerical test cases including a vortex advection, supersonic compressible flow over a cylinder, Poiseuille flow, turbulent channel and pipe flows. The results obtained here are in an excellent agreement when compared to the experimental data and the previous direct numerical simulation (DNS). As for the DDM strategy, it was successful as simulation time is clearly decreased and the connection between the two subdomains does not create spurious oscillations. Originality/value In sum, the developed solver was capable of solving, accurately and with high-precision, two- and three-dimensional compressible flows including fairly complex geometries. It is noted that the data provided by the DNS of supersonic pipe flows are not abundant in the literature and therefore will be available online for the community.

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