Adjoint error estimation for EHL‐like models

Hart, Dan; Goodyer, Christopher E.; Berzins, Martin; Jimack, Peter K.; Scales, L. E.

doi:10.1002/fld.881

Cited by 3 publications

(4 citation statements)

References 5 publications

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“…The general issue of controlling the global error in time dependent PDE calculations remains problematic despite many recent successful algorithms based upon adjoint methods; see [5,26]. Adjoint methods are also important for EHL problems in that they provide a means of controlling the error in quantities of interest such as friction [20]. The key issue for large scale engineering calculations is the cost of the estimation algorithms.…”

Section: Space and Time Error Estimation And Balancingmentioning

confidence: 99%

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Adaptive Timestepping for Elastohydrodynamic Lubrication Solvers

Goodyer¹,

Berzins²

2006

SIAM J. Sci. Comput.

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The application of variable-step time-integration techniques in a method of lines approach for the numerical solution of transient elastohydrodynamic lubrication calculations is described. Spatial discretization of the coupled integro-differential equations leads to a system of differential-algebraic equations in time. At each timestep a large system of nonlinear equations of 10 4-10 7 variables is solved by using multigrid methods and multilevel multi-integration. The application of temporal error control methods is considered with reference to both the differential-algebraic formulation of the system to be solved and the multigrid-based nonlinear equation solver to be used. The error control method used takes account of the magnitude of the spatial error present by using a local time error control based on the magnitude of this error. This approach is shown to be beneficial in reducing the computational work required. Experimental results on a variety of lubrication problems, including a challenging rough surface problem, are used to display the effectiveness of the methods.

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Section: Space and Time Error Estimation And Balancingmentioning

confidence: 99%

“…Future work in this area should consider the use of adjoint-based approaches with regard to the direct estimation and control of errors in quantities such as the central and minimum film thicknesses, or other quantities of interest such as the friction [17,20].…”

Section: Real Surface Roughnessmentioning

confidence: 99%

Adaptive Timestepping for Elastohydrodynamic Lubrication Solvers

Goodyer¹,

Berzins²

2006

SIAM J. Sci. Comput.

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“…Our approach is to build upon an earlier, exploratory study [3] which applied the techniques used here (based upon [4][5][6]) to a simple model problem. The contribution of this paper is to show that 1560 D. E. HART ET AL. this methodology can be extended successfully to the full EHL problem with a realistic model of film thickness and the application of adaptive meshes.…”

Section: Introductionmentioning

confidence: 99%

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

Hart

Berzins

Goodyer

et al. 2010

Numerical Methods in Fluids

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SUMMARYThe use of an adjoint technique for goal-based error estimation described by Hart et al. (Int. J. Numer. Meth. Fluids 2005; 47:1069-1074) is extended to the numerical solution of free boundary problems that arise in elastohydrodynamic lubrication (EHL). EHL systems are highly nonlinear and consist of a thinfilm approximation of the flow of a non-Newtonian lubricant which separates two bodies that are forced together by an applied load, coupled with a linear elastic model for the deformation of the bodies. A finite difference discretization of the line contact flow problem is presented, along with the numerical evaluation of an exact solution for the elastic deformation, and a moving grid representation of the free boundary that models cavitation at the outflow in this one-dimensional case. The application of a goal-based error estimate for this problem is then described. This estimate relies on the solution of an adjoint problem; its effectiveness is demonstrated for the physically important goal of the total friction through the contact. Finally, the application of this error estimate to drive local mesh refinement is demonstrated.

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“…For simplicity the mesh spacing may be considered to be fixed, at X ∆ say, although in practice it will be allowed to adapt in different regions of the domain. In order to satisfy (10) it is necessary to allow c X to vary until both the discrete forms of (7) and (10) are satisfied together (achieved via an iterative procedure). Other approaches to dealing with the cavitation region may be found elsewhere (which would make the sparsity pattern of the Jacobian matrix in (5) dense) and also, with the extension to deforming contacts in mind, eliminates the need to recompute the kernel function.…”

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confidence: 99%

Adjoint Error Estimation and Spatial Adaptivity for EHL-Like Models

Hart

Goodyer

Berzins

et al.

IUTAM Symposium on Elastohydrodynamics and Micro-Elastohydrodynamics

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Abstract:The use of adjoint error estimation techniques is described for a model problem that is a simplified version of an EHL line contact. Quantities of interest, such as friction, may be dependent upon the accuracy of the solution in some parts of the domain more than in others. The use of an inexpensive extra solve to calculate an adjoint solution is described for estimating the intergrid error in the value of friction calculated, and as a basis for local refinement. It is demonstrated that this enables an accurate estimate for the quantity of interest to be obtained from a less accurate solution of the model problem.

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Adjoint error estimation for EHL‐like models

Cited by 3 publications

References 5 publications

Adaptive Timestepping for Elastohydrodynamic Lubrication Solvers

Adaptive Timestepping for Elastohydrodynamic Lubrication Solvers

Using adjoint error estimation techniques for elastohydrodynamic lubrication line contact problems

Adjoint Error Estimation and Spatial Adaptivity for EHL-Like Models

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