Large Eddy Simulations using High order Flux Reconstruction method on Hybrid Unstructured meshes

2014 ◽  
Author(s):  
Yi LU ◽  
William N. Dawes
Keyword(s):  
Unstructured Meshes ◽  
High Order ◽  
Large Eddy Simulations ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Large Eddy

Large Eddy Simulations for 3D Turbine Blades Using a High Order Flux Reconstruction Method

2013 ◽  
Author(s):  
Yi Lu ◽  
Kai Liu ◽  
W. N. Dawes
Keyword(s):  
Turbine Blade ◽  
High Order ◽  
Large Eddy Simulations ◽  
Complex Geometries ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Order Accuracy ◽  
Local Reconstruction ◽  
Low Pressure Turbine ◽  
Large Eddy

During the last decades, the improvements of both computational ability and numerical schemes have stimulated increasing industrial interest in the use of Large Eddy Simulations (LES) for practical engineering flow problems. However, almost all current approches cannot treat complex geometries at affordable cost to enable LES of industrial problems. A robust, parallel and efficient solver using a general unstructured grid & based on high order flux reconstruction formulation, which uses local reconstruction, is compact and written in differential form without a mass matrix, was developed and has proved the ability to get accurate LES results but using RANS scale meshes. This work is aimed at using flux reconstruction method to perform Large Eddy Simulations for complex geometries in more robust and highly efficient way. Both explicit Runge-Kutta method and implicit LU-SGS method are implemented with improvements as solvers for better performance on boundary layer meshes including large aspect ratio cells. The current solver is ported to GPU architectures and speed up ratios of different order accuracy are presented in this work. A local reconstruction method is introduced to generate high order curved boundary from readily available first order meshes. The large eddy simulations for low pressure turbine blade and low pressure turbine blade with endwall are presented in this work, resolved with total number of degree of freedoms up to 34 million to chieve fourth order accuracy using limited computational resource. The results show that this approach has the potential to obtain LES results of real-geometry problems with affordable computational costs.

High Order Large Eddy Simulations for a Transonic Turbine Blade Using Hybrid Unstructured Meshes

2015 ◽  
Author(s):  
Yi Lu ◽  
W. N. Dawes
Keyword(s):  
Turbine Blade ◽  
Unstructured Meshes ◽  
Large Eddy Simulations ◽  
Flux Reconstruction ◽  
Flow Problems ◽  
Time Stepping ◽  
Large Eddy ◽  
Local Time Stepping ◽  
Time Extension ◽  
Transonic Turbine

Large eddy simulations were performed for a transonic turbine blade on hybrid unstructured meshes. High order accuracy in both space and time discretization is achieved by using a space time extension of flux reconstruction method(STEFR), and in particular, local time-stepping is enabled for time-accurate unsteady simulations. A piecewise integration in-cell method is introduced for shock-capturing within the STEFR method. This method is completely local in both space and time directions, without any explicit addition to the discretisation, which is suitable for the predictor-corrector type space time extension allowing local timestepping. A volume averaged compensation method is used to construct a conservative form of the Chain-Rule scheme for the flux divergence part of the flux reconstruction discretisation, which is proved stable and efficient to solve flow problems with physical discontinuities. This work successfully extends the application of the STEFR method to solve transonic/supersonic unsteady flows. The numerical validation for the 1D burgers equation and its comparison with traditional multi-stage Runge-Kutta method with uniform time-stepping, indicate that this piecewise integration in-cell method is accurate and more robust with STEFR method using local time-stepping. A significant advantage of this method is the successfully implementation on hybrid unstructured meshes, which makes it very efficient and scalable to solve multi-scale, complex geometries flow problems. The moving shock, shock-boundary layer interaction, shock-wake interaction were crisply resolved and analyzed for the transonic turbine blade, VKI-LS59, and detail post-processing is presented with the comparison with experimental data in this paper.

A High-Order Flux Reconstruction Method for 2-D Vorticity Transport

2021 ◽  
Author(s):  
Adrin Gharakhani
Keyword(s):  
Finite Difference ◽  
Poisson Equation ◽  
Finite Difference Methods ◽  
Neumann Boundary ◽  
Normal Derivative ◽  
High Order ◽  
Benchmark Problems ◽  
Flux Reconstruction ◽  
Reconstruction Method ◽  
Vorticity Transport

Abstract A compact high-order finite difference method on unstructured meshes is developed for discretization of the unsteady vorticity transport equations (VTE) for 2-D incompressible flow. The algorithm is based on the Flux Reconstruction Method of Huynh [1, 2], extended to evaluate a Poisson equation for the streamfunction to enforce the kinematic relationship between the velocity and vorticity fields while satisfying the continuity equation. Unlike other finite difference methods for the VTE, where the wall vorticity is approximated by finite differencing the second wall-normal derivative of the streamfunction, the new method applies a Neumann boundary condition for the diffusion of vorticity such that it cancels the slip velocity resulting from the solution of the Poisson equation for the streamfunction. This yields a wall vorticity with order of accuracy consistent with that of the overall solution. In this paper, the high-order VTE solver is formulated and results presented to demonstrate the accuracy and convergence rate of the Poisson solution, as well as the VTE solver using benchmark problems of 2-D flow in lid-driven cavity and backward facing step channel at various Reynolds numbers.

scholarly journals Performance of high-order implicit large eddy simulations

2018 ◽  
Vol 173 ◽  
pp. 307-312 ◽  
Author(s):  
Konstantinos Ritos ◽  
Ioannis W. Kokkinakis ◽  
Dimitris Drikakis
Keyword(s):  
High Order ◽  
Large Eddy Simulations ◽  
Large Eddy
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