Abstract



A method will be described to accelerate timedependent numerical solvers of PDEs that is based on the combined use of proper orthogonal decomposition (POD) and Galerkin projection. POD is made on some sets of snapshots that are calculated using the numerical solver, and the governing equations are Galerkinprojected onto the PODcalculated modes. Snapshots calculation and Galerkin projection are made in interpersed time intervals. Switching between both is made using an a priori error estimate that provides quite good results. Several additional improvements make the method both robust and computationally e±cient. The method will be applied to two onedimensional problems, a timedependent Fisher equation and the complex the GinzburgLandau (GL) equation. In these two cases results are excellent, even in cases in which the GL equation exhibits transient chaos; compression factors (measuring the ratio of the total time span to the total length of the time intervals in which the full numerical solver is applied) are of the order of 10, and can be increased to 80 using a snapshots library to initiate the process. Application will also be made to a twodimensional problem, namely the pulsating cavity problem, which describes the motion of liquid in a square box whose upper wall is moving back and forth in a quasiperiodic fashion. In this case, the numerical solver will be based on a rough (but quick) computational °uid dynamics (CFD) code that resembles those (industrial) codes that are usually used in Industry. Consequently, it is the numerical code and not the governing equations themselves that is projected into the POD modes. Results are again excellent; compression factors are again of the order of 10 and are increased using a snapshots library. Projection of the exact governing equations will also be considered. Several consequences of all these will be brie°y discussed.  
International

Si 

Pendiente 
Entity

Universidad de Barcelona 
Entity Nationality

ESPAÑA 
Place

Barcelona 