A parallel, non-spatial iterative, and rotational pressure projection method for the nonlinear fluid-fluid interaction

2021 ◽  
Vol 165 ◽  
pp. 119-136
Author(s):  
Jian Li ◽  
Jiawei Gao ◽  
Yu Shu
Keyword(s):  
Projection Method ◽  
Pressure Projection ◽  
Fluid Interaction ◽  
Nonlinear Fluid

A linear, decoupled fractional time‐stepping method for the nonlinear fluid–fluid interaction

2019 ◽  
Vol 35 (5) ◽  
pp. 1873-1889 ◽  
Author(s):  
Jian Li ◽  
Pengzhan Huang ◽  
Chong Zhang ◽  
Gaihui Guo
Keyword(s):  
Time Stepping ◽  
Fluid Interaction ◽  
Nonlinear Fluid

A Pressure Projection Method for Nearly Incompressible Rubber Hyperelasticity, Part I: Theory

1996 ◽  
Vol 63 (4) ◽  
pp. 862-868 ◽  
Author(s):  
Jiun-Shyan Chen ◽  
Chunhui Pan
Keyword(s):  
Hydrostatic Pressure ◽  
Energy Density ◽  
Least Squares ◽  
Projection Method ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Least Squares Method ◽  
Finite Element Program ◽  
Reduced Integration ◽  
Pressure Projection

A least-squares-based pressure projection method is proposed for the nonlinear analysis of nearly incompressible hyperelastic materials. The strain energy density function is separated into distortional and dilatational parts by the use of Penn’s invariants such that the hydrostatic pressure is solely determined from the dilatational strain energy density. The hydrostatic pressure and hydrostatic pressure increment calculated from displacements are projected onto appropriate pressure fields through the least-squares method. The method is applicable to lower and higher order elements and the projection procedures can be implemented into the displacement based nonlinear finite element program. By the use of certain pressure interpolation functions and reduced integration rules in the pressure projection equations, this method can be degenerated to a nonlinear version of the selective reduced integration method.

scholarly journals High-order consistent SPH with the pressure projection method in 2-D and 3-D

2021 ◽  
pp. 110563
Author(s):  
A.M.A. Nasar ◽  
G. Fourtakas ◽  
S.J. Lind ◽  
J.R.C. King ◽  
B.D. Rogers ◽  
...  
Keyword(s):  
Projection Method ◽  
High Order ◽  
Pressure Projection

A Pressure Projection Method for Nearly Incompressible Rubber Hyperelasticity, Part II: Applications

1996 ◽  
Vol 63 (4) ◽  
pp. 869-876 ◽  
Author(s):  
Jiun-Shyan Chen ◽  
Cheng-Tang Wu ◽  
Chunhui Pan
Keyword(s):  
Finite Element ◽  
Energy Density ◽  
Projection Method ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Finite Elasticity ◽  
Element Formulation ◽  
Density Functions ◽  
Hyperelastic Materials ◽  
Pressure Projection

In the first part of this paper a pressure projection method was presented for the nonlinear analysis of structures made of nearly incompressible hyperelastic materials. The main focus of the second part of the paper is to demonstrate the performance of the present method and to address some of the issues related to the analysis of engineering elastomers including the proper selection of strain energy density functions. The numerical procedures and the implementation to nonlinear finite element programs are presented. Mooney-Rivlin, Cubic, and Modified Cubic strain energy density functions are used in the numerical examples. Several classical finite elasticity problems as well as some practical engineering elastomer problems are analyzed. The need to account for the slight compressibility of rubber (finite bulk modulus) in the finite element formulation is demonstrated in the study of apparent Young’s modulus of bonded thin rubber units. The combined shear-bending deformation that commonly exists in rubber mounting systems is also analyzed and discussed.

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