Research Development on Fish Swimming

Chinese Journal of Mechanical Engineering

Table 2 Main CFD methods applied in fish locomotion

CFD method	Description	Representative
Conventional method	Finite volume approach for Navier-Stokes equation; Fluent use-defined function for Newton equation; Staggered integration algorithm for coupled system	Koumoutsakos [48]; Xia Dan [49,50,−51]; Ningyu Li [52, 53]
Remeshed vortex method	A penalization technique for the no-slip boundary condition and a projection method for the action from fluid to body	Koumoutsakos [54, 55]
MPCDM	Only for low Reynolds numbers	Reid [56]
LS-IIM	Level-set function for solid-fluid interface	Thekkethil [57]
FuRMoRP	Distributed Lagrange multipliers methods for rigid and flexible bodies	Patankar [58]
Delta-plus-SPH	Delta-plus-SPH scheme for numerical accuracy and efficiency	Sun [59]
IBM
Pure IBM	For idealized object like jellyfish or rigid foil	Battista [60,61,62,−63]; Hemmati [64]
IBAMR	Cartesian grid adaptive mesh refinement (AMR) for motion equation discretization	Patankar [32, 65]; Pan Guang [66, 67]
LS-IBM	Level-set function for solid-fluid interface	Atul Sharma [68, 69]; Cui Zuo [70,71,−72]
Sharp interface IBM	A discrete-forcing scheme a ‘‘sharp” representation of the immersed boundary	Dong Haibo [73,74,−75]
BDIM	The field equations of whole domain are combined analytically	Weymouth [76, 77]
HCIB	Hybrid staggered/non-staggered mesh formulation for boundary conditions	Borazjani [78]
Other methods	A uniform Cartesian grid for Poisson equation and volume penalization method for deformable body	Ghaffari [79]; Bergmann [80]

Note: HCIB: Hybrid Cartesian/immersed boundary method; LS-IIM: A level-set function based immersed interface method; FuRMoRP: Fully resolved momentum redistribution for self-Propulsion algorithm; BDIM: Boundary Data Immersion Method; MPCDM: Multiparticle collision dynamics model.