Problems involving fluid flexible-structure interactions(FFSI)are ubiquitous in engineering and sciences.Peskin’s immersed boundary(IB)method is the first framework for modeling and simulation of such problems.This p...Problems involving fluid flexible-structure interactions(FFSI)are ubiquitous in engineering and sciences.Peskin’s immersed boundary(IB)method is the first framework for modeling and simulation of such problems.This paper addresses a three-dimensional extension of the IB framework for non-Newtonian fluids which include power-law fluid,Oldroyd-B fluid,and FENE-P fluid.The motion of the non-Newtonian fluids are modelled by the lattice Boltzmann equations(D3Q19 model).The differential constitutive equations of Oldroyd-B and FENE-P fluids are solved by the D3Q7 model.Numerical results indicate that the new method is first-order accurate and conditionally stable.To show the capability of the new method,it is tested on three FFSI toy problems:a power-law fluid past a flexible sheet fixed at its midline,a flexible sheet being flapped periodically at its midline in an Oldroyd-B fluid,and a flexible sheet being rotated at one edge in a FENE-P fluid.展开更多
基金The work is supported by the US National Science Foundation(NSF)through the research grant DMS-1522554We thank the unknown Reviewers for their helpful suggestions and comments which have helped us.
文摘Problems involving fluid flexible-structure interactions(FFSI)are ubiquitous in engineering and sciences.Peskin’s immersed boundary(IB)method is the first framework for modeling and simulation of such problems.This paper addresses a three-dimensional extension of the IB framework for non-Newtonian fluids which include power-law fluid,Oldroyd-B fluid,and FENE-P fluid.The motion of the non-Newtonian fluids are modelled by the lattice Boltzmann equations(D3Q19 model).The differential constitutive equations of Oldroyd-B and FENE-P fluids are solved by the D3Q7 model.Numerical results indicate that the new method is first-order accurate and conditionally stable.To show the capability of the new method,it is tested on three FFSI toy problems:a power-law fluid past a flexible sheet fixed at its midline,a flexible sheet being flapped periodically at its midline in an Oldroyd-B fluid,and a flexible sheet being rotated at one edge in a FENE-P fluid.
