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 Author Valivarthi, Mohan Varma Title A Finite Element Time Relaxation Method URL http://urn.kb.se/resolve?urn=urn:nbn:se:hh:diva-17728 Publication Date 2012 Discipline/Department Computer and Electrical Engineering (IDE) University/Publisher Halmstad University Abstract In our project we discuss a finite element time-relaxation method for high Reynolds number flows. The key idea consists of using local projections on polynomials defined on macro element of each pair of two elements sharing a face. We give the formulation for the scalar convection–diffusion equation and a numerical illustration. Subjects/Keywords high Reynolds flow; time relaxation; local projections; convection-diffusion equation Language en Country of Publication se Record ID oai:DiVA.org:hh-17728 Other Identifiers Local IDE1222 Repository diva Date Indexed 2020-01-03

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…method can be better handled in a wide variety of elements and mesh topologies. A new stabilized finite element method for the Stokes problem is established, based on local L2 pressure projection [13]. These projections are introduced in order…

…velocity pairs. One of the main advantages of this method is the computations of pressure projections and the penalty form is completely local. The method based on polynomial projections leads to symmetric linear systems and independent of mesh-dependent…

projections in the mixed bilinear form are used. However still it is observed that a pair of the form such as P1-P0 which is formally consistent but unstable. It is clear that eliminating the velocity-pressure inconsistency alone may not be enough to ensure…

…stability. In this stabilization approach, in addition to local pressure projection an additional term is added that penalizes pressure deviation from the consistent polynomial order, which makes the problem remain stable for all equal- order pressure…

…space contains the set of polynomials of maximal total degree k, Pk. Also we introduce the local polynomial spaces Wl ( ̂ ) : = { w ∈ Pl( ̂ )}, l ≥0. and We define the scalar products ( f , g)Ω := ʃΩ fg dx and…

…addition of proposed time-relaxation method. 20 6. Conclusion A simplified time relaxation method for high Peclet number flows is proposed and tested numerically. Our method is a completely local implementation, implemented on a patch consisting of…

projections. Int. J. Numer. Meth. Fluids, 46: 183–201. doi: 10.1002/fld.752. 14.R. Becker et al., A finite element time relaxation method, C R Acad. Sci. Paris, Ser. I (2011), doi: 10.1016/j.crma.2010.12.010. 15.Brooks, A.N.; Hughes, T.J.R…

…x29;]; ynodn = [ynod; ynew(1:(nno - nold))]; For the sub function “neighbours” : function nei = neighbours(nodes) % % 'nei' contains the four neighbours to each element in local order of '…