INVESTIGADORES
NIGRO Norberto Marcelo
congresos y reuniones científicas
Título:
IMPROVEMENTS TO SOLVE DIFFUSION-DOMINANT PROBLEMS WITH PFEM-2
Autor/es:
GIMENEZ JUAN; NIGRO NORBERTO; IDELSOHN, SERGIO
Lugar:
Salta
Reunión:
Congreso; MECOM 2012; 2012
Institución organizadora:
AMCA
Resumen:
Particle Finite Element Method - Second generation (PFEM-2) is a method characterized byusing both particles and mesh to solve physics equations.In some previous papers the mathematical and numerical basis of the method with also someresults were presented showing a good accuracy and high performance for solving scalar-transport andmomentum-transport problems with dominant advection term.To preserve accurate solutions on the mesh, the method must create or remove particles to haveenough information to solve diffusive terms. In these problems and under certain types of velocity fieldsand/or mesh, some cautions at the particle-updating step must be taken into account to avoid an excessivenumerical diffusion in the solutions. In this way, an improved approach to create and remove particles ispresented here.Moreover, when the problem is diffusion-dominant, the advantages of the method are not as clear asin the advection-dominant cases. The explicit calculation of the diffusion traditionally used by PFEM-2is limited by the dimensionless Fourier number and, in some particular cases, the method may fail. Torelax these restrictions, a new model to calculate the diffusion is developed. It is based on the thetamethod which consists on discretizing the non-stationary variable using a weighted mixture between anexplicit prediction and an implicit correction. This approach extends the stability limit, while reducingthe error, and it could also allow the usage of longer time steps. Even though the implicit may becomputationally expensive, exploiting the possibility of factorizing the matrix at the beginning and usingit as a preconditioner for solving the diffusion step had shown to have good performance.To validate the solutions proposed here some tests are solved comparing their different results withthe analytic ones. This report is focused on showing how the new models improve the accuracy of thesolutions of the older ones and how the computing times are modified.