The derivation of transport
of the Fluid Particle Model
for non-linear constitutive equation
Maciej Paszyński, mp(at)robobat.pl
Robert Schaefer, schaefer(at)softlab.ii.uj.edu.pl
Jagiellonian University, Institute of Computer Science, Nawojki 11, 30-072 Cracow, Poland
Abstract: The paper presents the theoretical studies of the modification of the Fluid Particle Model (FPM) that allows to simulate the flow of the fluid described by non-linear constitutive equations. The general consideration is dedicated to the blood flow described by the non-linear Casson formula. The problem of three dimensional modeling of pulsatille blood flow in cardiovascular system in man is of the great importance in medicine and biology.
Fluid Particle Model invented by Español allows to overcome many problems arising in classical methods (e.g. Finite Elements Method and Finite Differences Method). Rheological properties of the fluid are expressed by inter-particle forces in the FPM method. The proposed modification of FPM consists in applying the successively linearized constitutive formula instead of the linear one by computing inter-particle forces.
The main theoretical result of this paper consists in derivation of transport coefficients from the modified inter-particle forces, taking into account the non-linear Casson stress
derivation.ps (367 K),
derivation.pdf (212 K)