Moving grid

Ren, N. and Lee, S., Gontact Simulation of Three-Dimensional Rough Surfaces Using Moving Grid Method, ASMEJ. Tribol,Vol. 115,1993,pp.597-601. 

RANS codes were not unsuccessful for the study of piston engines [25-27]. However, it is only with LES [30], for example, that the study of cycle-to-cycle variations becomes possible. For such studies, the solver must have moving-grid capabilities for the piston and the valves, while retaining all the required properties for LES, such as a high-order numerical method. From the point of view of modeling, the combustion model must handle... 

A. Madzvamuse, A.J. Wathen, P. Maini, A moving grid finite element method applied to a model biological pattern generator, J. Comput. Phys. 190 (2003) 478-500. 

Attarakih M, Bart HJ, Faqir NM. An approximate optimal moving-grid technique for the solution of discretized population balances in batch systems. Proceedings of ESCAPE 12 European Symposium on Computer-Aided Process Engineering, The Hague, 2002. 

In moving-grid methods, the interface is a boundary between two subdomains of the grid. The interface then identifies, at some order of approximation, with boundaries of elements into which the phases are discretized. When the interface undergoes large deformations, the grid has to be remeshed. 

V. Moureau, G. Lartigue, Y. Sommerer, C. Angelberger, O. Colin, and T. Poinsot. High-order methods for DNS and LES of compressible multi-component reacting flows on fixed and moving grids. J. Comput. Phys., 202(2) 710-736, 2005. 

Tryggvason and co-workers [227, 228, 127, 128, 170, 224, 71, 72, 225] solve the Navier-Stokes equations using a projection method very similar to the MAC method [96]. The interface is tracked explicitly by connected marker points. In the solution procedure a fixed structured grid is used for the transport equations, and a moving grid of lower dimension marks the boundary between the bulk phases. This moving grid is called the front. 

Thrust propulsive force developed by a jet-propeller motor N) u control volume surface velocity arising from the motion of the moving grid m/s)... 

Fig. 17.2 Numerical methods for the fluid flow with moving free surface. Moving grids (a) Lagrangian FE method, and fixed grids (b) MAC method and (c) VOF method [16] (Courtesy of John Wiley and Sons)...

K. L. Bieniasz. Use of dynamically adaptive grid techniques for the solution of electrochemical kinetic equations Part 1. Introductory exploration of the finite-difference adaptive moving grid solntion of the one-dimensional fast homogeneons reaction-diffnsion problem with a reaction layer, J. Electroanal. Chem. 360, 119-138 (1993). 

J. G. Blom, J. M. Sanz-Serna, and J. G. Verwer. On simple moving grid methods for one-dimensional evolntionary partial differential equations, J. Comput. Phys. 74, 191-213 (1988). 

Numerical Techniques for Free Surface Flows Inter- free surface. Moving grids (a) Lagiangian FE method,... 

A quite popular and widely used approach to increase robustness and efficiency of a MOL treatment of PDE problems is the use of a moving grid. One may distinguish two different categories of moving grid techniques. (I) The nodes of the grid are moved such that the values of a certain monitor function are equidistributed in space - see e.g. [1, 2, 5, 17]. (II) The nodes are moved to reduce the dynamics of the solution on the new coordinates see... 

With this general equation and A in the range [0.01,0.25] quite good results for a set of typical test problems can be obtained. Even better results are obtained by using special moving grid equations, e.g. fixing one node to a special solution value. 

Petzold, L. R., An adaptive Moving Grid Method for One-Dimensional Systems of Partial Differential Equations and its Numerical Solution, Proc. Workshop on Adaptive Methods for Partial Differential Equations, Renselaer Polytechnic Institute (1988)... 

Verwer, J.G., Blom, J.G. and Sanz-Sema, 1981, An adaptive moving grid method for one-dimensional systems of partial differential equations. Journal of Computational Physics, 83(2), 454-486. 

Zegeling, P.A. Moving-Grid Methods for Time-Dependent Partial Differential Equations, CWI Tract, Amsterdam, 1993. Also avaUable at http //www.math. uu.nl/people/zegeling/publist.html. 

Blom JG, Sanz-Serna IM, Verwer IG (1988) On simple moving grid methods for onedimensional evolutionary partial differential equations. J Comput Phys 74 191-213... 

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