Third-order Cartesian overset mesh adaptation method for solving steady compressible flows

2008 ◽  
Vol 57 (7) ◽  
pp. 811-838 ◽  
Author(s):  
O. Saunier ◽  
C. Benoit ◽  
G. Jeanfaivre ◽  
A. Lerat
Keyword(s):  
Compressible Flows ◽  
Mesh Adaptation ◽  
Third Order ◽  
Adaptation Method

scholarly journals A feature-based mesh adaptation for the unsteady high speed compressible flows in complex three-dimensional domains

2016 ◽  
Vol 40 (3) ◽  
pp. 1728-1740
Author(s):  
Hoang-Huy Nguyen ◽  
Vinh-Tan Nguyen ◽  
Matthew A. Price ◽  
Oubay Hassan
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Three Dimensional ◽  
Mesh Adaptation ◽  
Feature Based

A goal-oriented anisotropic hp-mesh adaptation method for linear convection–diffusion–reaction problems

2019 ◽  
Vol 78 (9) ◽  
pp. 2973-2993 ◽  
Author(s):  
Ondřej Bartoš ◽  
Vít Dolejší ◽  
Georg May ◽  
Ajay Rangarajan ◽  
Filip Roskovec
Keyword(s):  
Mesh Adaptation ◽  
Diffusion Reaction ◽  
Convection Diffusion ◽  
Adaptation Method

scholarly journals Scalability of OpenFOAM Density-Based Solver with Runge–Kutta Temporal Discretization Scheme

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Sibo Li ◽  
Roberto Paoli ◽  
Michael D’Mello
Keyword(s):  
Compressible Flows ◽  
Large Scale ◽  
National Laboratory ◽  
Time Integration ◽  
Argonne National Laboratory ◽  
Euler Scheme ◽  
Third Order ◽  
Runge Kutta ◽  
Unsteady Problems ◽  
Large Scale Simulations

Compressible density-based solvers are widely used in OpenFOAM, and the parallel scalability of these solvers is crucial for large-scale simulations. In this paper, we report our experiences with the scalability of OpenFOAM’s native rhoCentralFoam solver, and by making a small number of modifications to it, we show the degree to which the scalability of the solver can be improved. The main modification made is to replace the first-order accurate Euler scheme in rhoCentralFoam with a third-order accurate, four-stage Runge-Kutta or RK4 scheme for the time integration. The scaling test we used is the transonic flow over the ONERA M6 wing. This is a common validation test for compressible flows solvers in aerospace and other engineering applications. Numerical experiments show that our modified solver, referred to as rhoCentralRK4Foam, for the same spatial discretization, achieves as much as a 123.2% improvement in scalability over the rhoCentralFoam solver. As expected, the better time resolution of the Runge–Kutta scheme makes it more suitable for unsteady problems such as the Taylor–Green vortex decay where the new solver showed a 50% decrease in the overall time-to-solution compared to rhoCentralFoam to get to the final solution with the same numerical accuracy. Finally, the improved scalability can be traced to the improvement of the computation to communication ratio obtained by substituting the RK4 scheme in place of the Euler scheme. All numerical tests were conducted on a Cray XC40 parallel system, Theta, at Argonne National Laboratory.

scholarly journals Mesh Adaptation Method for Optimal Control With Non-Smooth Control Using Second-Generation Wavelet

IEEE Access ◽  
2019 ◽  
Vol 7 ◽  
pp. 135076-135086
Author(s):  
Zhiwei Feng ◽  
Qingbin Zhang ◽  
Jianquan Ge ◽  
Wuyu Peng ◽  
Tao Yang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Second Generation ◽  
Mesh Adaptation ◽  
Smooth Control ◽  
Second Generation Wavelet ◽  
Adaptation Method

scholarly journals Entropy dissipation of moving mesh adaptation

2014 ◽  
Vol 11 (03) ◽  
pp. 633-653 ◽  
Author(s):  
Mária Lukáčová-Medvid'ová ◽  
Nikolaos Sfakianakis
Keyword(s):  
Numerical Stability ◽  
Sufficient Conditions ◽  
Mesh Adaptation ◽  
Moving Mesh ◽  
Nonlinear Conservation Laws ◽  
The Past ◽  
Entropy Dissipation ◽  
Uniform Grids ◽  
Mesh Reconstruction ◽  
Adaptation Method

Non-uniform grids and mesh adaptation have become an important part of numerical approximations of differential equations over the past decades. It has been experimentally noted that mesh adaptation leads not only to locally improved solution but also to numerical stability of the underlying method. In this paper we consider nonlinear conservation laws and provide a method to perform the analysis of the moving mesh adaptation method, including both the mesh reconstruction and evolution of the solution. We moreover employ this method to extract sufficient conditions — on the adaptation of the mesh — that stabilize a numerical scheme in the sense of the entropy dissipation.

Least-squares finite element solution of Euler equations with H-type mesh refinement and coarsening on triangular elements

2014 ◽  
Vol 24 (7) ◽  
pp. 1487-1503 ◽  
Author(s):  
Hayri Yigit Akargun ◽  
Cuneyt Sert
Keyword(s):  
Finite Element ◽  
Least Squares ◽  
Euler Equations ◽  
Compressible Flows ◽  
Mesh Refinement ◽  
Mesh Adaptation ◽  
Content Type ◽  
Triangular Elements ◽  
Inviscid Compressible Flows ◽  
Mesh Coarsening

Purpose – The purpose of this paper is to demonstrate successful use of least-squares finite element method (LSFEM) with h-type mesh refinement and coarsening for the solution of two-dimensional, inviscid, compressible flows. Design/methodology/approach – Unsteady Euler equations are discretized on meshes of linear and quadratic triangular and quadrilateral elements using LSFEM. Backward Euler scheme is used for time discretization. For the refinement of linear triangular elements, a modified version of the simple bisection algorithm is used. Mesh coarsening is performed with the edge collapsing technique. Pressure gradient-based error estimation is used for refinement and coarsening decision. The developed solver is tested with flow over a circular bump, flow over a ramp and flow through a scramjet inlet problems. Findings – Pressure difference based error estimator, modified simple bisection method for mesh refinement and edge collapsing method for mesh coarsening are shown to work properly with the LSFEM formulation. With the proper use of mesh adaptation, time and effort necessary to prepare a good initial mesh reduces and mesh independency control of the final solution is automatically taken care of. Originality/value – LSFEM is used for the first time for the solution of inviscid compressible flows with h-type mesh refinement and coarsening on triangular elements. It is shown that, when coupled with mesh adaptation, inherent viscous dissipation of LSFEM technique is no longer an issue for accurate shock capturing without unphysical oscillations.

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