Efficient Adjoint-Based Mesh Adaptation Applied to Turbo-Machinery Flows

2018 ◽  
Author(s):  
Guglielmo Vivarelli ◽  
Ning Qin ◽  
Shahrokh Shahpar ◽  
David Radford
Keyword(s):  
Mesh Refinement ◽  
Mesh Adaptation ◽  
Spring Stiffness ◽  
Mesh Movement ◽  
Industrial Setting ◽  
Flow Features ◽  
Refinement Procedure ◽  
Turbo Machinery ◽  
Quantities Of Interest

Within an industrial setting, mesh adaptation has so far found very limited use. This is, in part, due to the complexity of the geometries and flow features that are to be dealt with. However, the successful utilisation of grid modification techniques, could help engineers achieve more accurate estimates of quantities of interest quickly and efficiently. For this reason, in this paper, adjoint error mesh adaptation technology is developed and applied to steady-3D turbo-machinery solutions. The grid modification strategy proposed comprises of a combined mesh movement and mesh refinement procedure, entirely based on errors related to the functional of interest. The node addition scheme makes use of the output to the flow adjoint solver and an interpolation to an embedded grid. The determined error is used in an edge-refinement approach developed in the in-house MeshPost software. The mesh relocation technique, instead, employs the sensitivity of the functional of interest with respect to the nodes’ coordinates to compute a Riemmannian metric. This parameter is then equi-distributed over the mesh by applying a spring-stiffness approach.

Using Feature-Based Mesh Adaptation to Improve the Adjoint Optimisation of Transonic Compressor Blades

2020 ◽  
Author(s):  
Alistair John ◽  
Guglielmo Vivarelli ◽  
Ning Qin ◽  
Shahrokh Shahpar
Keyword(s):  
Mesh Adaptation ◽  
Blade Design ◽  
Compressor Blades ◽  
Fine Grid ◽  
Transonic Compressor ◽  
Mesh Movement ◽  
Flow Features ◽  
Feature Based ◽  
First Time ◽  
Adaptation Method

Abstract The benefit of mesh adaptation to improve the optimisation process of turbomachinery components is here demonstrated for the first time. Mesh movement is used to automatically cluster and align the cells with significant flow features such as shocks, shock-induced separation and wakes for every geometry tested during a transonic compressor blade optimisation. Using mesh movement means that the same size grid is used while significantly improving the accuracy of the simulation and resulting adjoint gradients. A method is demonstrated to automatically carry out feature based mesh movement during every step of an adjoint optimisation process. Optimisations are carried out using the adaptation method and also using the starting mesh as a comparison. It is shown that (when tested on a very fine grid) the adaptation-optimisation process results in a better design, due to more accurate flow and gradient prediction throughout the optimisation process. A cost breakdown of the process is given to show that using adaptation during the optimisation process only increases the overall optimisation cost by a small amount, but results in greater efficiency of the final blade design.

scholarly journals Entropy-Based Mesh Refinement, II: A New Approach to Mesh Movement

2009 ◽  
Author(s):  
Daniel Zaide ◽  
Philip Roe
Keyword(s):  
Mesh Refinement ◽  
New Approach ◽  
Mesh Movement

scholarly journals Sequential feature‐based mesh movement and adjoint error‐based mesh refinement

2020 ◽  
Vol 93 (1) ◽  
pp. 249-272
Author(s):  
Guglielmo Vivarelli ◽  
Ning Qin ◽  
Shahrokh Shahpar ◽  
David Radford
Keyword(s):  
Mesh Refinement ◽  
Mesh Movement ◽  
Feature Based

scholarly journals Analysis of marking criteria for mesh adaptation in Cosserat elasticity

2018 ◽  
Vol 245 ◽  
pp. 08004 ◽  
Author(s):  
Maria Churilova
Keyword(s):  
Adaptive Mesh Refinement ◽  
Error Control ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Posteriori Error ◽  
Mesh Adaptation ◽  
Adaptive Meshes ◽  
A Posteriori Error ◽  
Cosserat Elasticity ◽  
Elasticity Problems

The article is devoted to comparison of finite element marking criteria for adaptive mesh refinement while solving plane Cosserat elasticity problems. The goal is to compare the resulting adaptive meshes obtained with different marking strategies. Mesh refinement and error control is done using the functional type a posteriori error majorant. Implemented algorithms use the zero-order Raviart-Thomas approximation on triangular meshes. Four widely used marking criteria are utilized for mesh adaptation. The comparative analysis is presented for two plane-strain problems.

New Adaptive Tools Dedicated to Surfacic Meshes Integrated Into a C.A.D. Environment

1994 ◽  
Author(s):  
Frédéric Noël ◽  
Jean-Claude Léon ◽  
Philippe Trompette
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Design Automation ◽  
Mesh Refinement ◽  
Mesh Adaptation ◽  
Free Form ◽  
Element Analysis ◽  
Geometric Data ◽  
Edge Swapping ◽  
Free Form Surfaces

Abstract The integration of CAD information and Finite Element Analysis is one of the important problems addressed by the design automation requirements. In case of parts involving free-form surfaces, the creation and adaptation of a mesh are still one of the bottlenecks attached to the search for competitive design. A solution is proposed which inserts a mesh adaptation software into the CAD-FEA chain. Full geometric data of free-form surfaces is used as input together with an initial approximate mesh. Geometric and mesh information on their own, as well as together, use extensively the concept of classification introduced here. Furthermore, topologically and geometrically layered adaptation tools are provided which achieve radaptivity, mesh coarsing, mesh refinement and edge swapping treatments. The toolkit thus available is demonstrated on examples and its integration requirements are all developed along its description.

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.

A non-standard mesh refinement procedure through node labelling

1984 ◽  
Vol 20 (7) ◽  
pp. 1361-1365 ◽  
Author(s):  
M. Fortin ◽  
P. Tanguy
Keyword(s):  
Mesh Refinement ◽  
Refinement Procedure

A Highly Accurate Approach That Resolves the Pressure Spike of Elastohydrodynamic Lubrication

1988 ◽  
Vol 110 (2) ◽  
pp. 241-246 ◽  
Author(s):  
E. J. Bissett ◽  
D. W. Glander
Keyword(s):  
Contact Problem ◽  
Numerical Method ◽  
Mesh Refinement ◽  
Elastohydrodynamic Lubrication ◽  
Length Scale ◽  
Line Contact ◽  
Small Length ◽  
Small Length Scale ◽  
Pressure Spike ◽  
Refinement Procedure

We propose an accurate numerical method to solve the classical line contact problem of elastohydrodynamic lubrication. The method incorporates a second order accurate discretization and a straightforward automatic local mesh refinement procedure. Using these elements, we remove discretization errors which have produced significant inaccuracies in previously published results, and we completely resolve the pressure spike which is shown to be smooth on a sufficiently small length scale.

An adaptive mesh refinement procedure for shape optimal design

1993 ◽  
Vol 18 (2) ◽  
pp. 131-145 ◽  
Author(s):  
J. Canales ◽  
J.A. Tárrago ◽  
A. Hernández
Keyword(s):  
Optimal Design ◽  
Adaptive Mesh Refinement ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Refinement Procedure
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