COMPARING THE SEMI-LAGRANGIAN INTEGRATION OF TRAJECTORIES IN MIXED FINITE ELEMENT SPACES THROUGH ONE- AND TWO-LEVEL TIME-STEPPING SCHEMES

Gustavo Peixoto de Oliveira¹; Eberson Luis de Souza Moraes²; José Pontes¹; Gustavo Anjos¹; Norberto Mangiavacchi¹

¹ State University of Rio de Janeiro; ² Federal University of Rio de Janeiro

doi:10.20906/CPS/COB-2015-0211

Resumo

Numerical simulations comparing the accuracy of trajectory integrators are presented in this work. The core methodology couples first- and second-order schemes with mixed finite element spaces used to discretize incompressible flow problems. Emphasis is given to a two-level time-stepping scheme which seeks intermediary values of the advected quantity to capture precisely the path of particles experiencing, specially, swirling or curved motions. Analises are organized regarding pairs of kind method/element, which bring up the overall differences between the called MINI and QUADratic element spaces, when associated to each of the semi-lagrangian integrators. The comparisons take into account the advection of a scalar concentrated in a two-dimensional domain which disperses away by the induction of a rotative velocity field.

Palavras-chave: Semi-lagrangian method; finite element; interpolation; numerical algorithm