Penalty finite element analysis of free surface flows of power-law fluids

1989 ◽  
Vol 24 (5) ◽  
pp. 383-399 ◽  
Author(s):  
M. Iga ◽  
J.N. Reddy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Free Surface ◽  
Power Law ◽  
Free Surface Flows ◽  
Element Analysis ◽  
Surface Flows ◽  
Power Law Fluids

Improved Implicit SPH Method for simulating free surface flows of power law fluids

2013 ◽  
Vol 56 (10) ◽  
pp. 2480-2490 ◽  
Author(s):  
YaWei Han ◽  
HongFu Qiang ◽  
QuanZhang Huang ◽  
JiuLing Zhao
Keyword(s):  
Free Surface ◽  
Power Law ◽  
Free Surface Flows ◽  
Sph Method ◽  
Surface Flows ◽  
Power Law Fluids ◽  
Implicit Sph

scholarly journals Variational analysis for simulating free-surface flows in a porous medium

2003 ◽  
Vol 2003 (8) ◽  
pp. 377-396
Author(s):  
Shabbir Ahmed ◽  
Charles Collins
Keyword(s):  
Finite Element ◽  
Porous Medium ◽  
Free Surface ◽  
Free Surface Flows ◽  
Parabolic Partial Differential Equation ◽  
Element Analysis ◽  
Surface Flows ◽  
The Matrix ◽  
The Stability ◽  
Positive Definite System

A variational formulation has been developed to solve a parabolic partial differential equation describing free-surface flows in a porous medium. The variational finite element method is used to obtain a discrete form of equations for a two-dimensional domain. The matrix characteristics and the stability criteria have been investigated to develop a stable numerical algorithm for solving the governing equation. A computer programme has been written to solve a symmetric positive definite system obtained from the variational finite element analysis. The system of equations is solved using the conjugate gradient method. The solution generates time-varying hydraulic heads in the subsurface. The interfacing free surface between the unsaturated and saturated zones in the variably saturated domain is located, based on the computed hydraulic heads. Example problems are investigated. The finite element solutions are compared with the exact solutions for the example problems. The numerical characteristics of the finite element solution method are also investigated using the example problems.

Natural frequency analysis of a functionally graded rotor-bearing system with a slant crack subjected to thermal gradients

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Arnab Bose ◽  
Prabhakar Sathujoda ◽  
Giacomo Canale
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Power Law ◽  
Beam Theory ◽  
Functionally Graded ◽  
Thermal Gradients ◽  
Element Analysis ◽  
Rotor Bearing ◽  
Natural Frequency Analysis ◽  
Bearing System

Abstract The present work aims to analyze the natural and whirl frequencies of a slant-cracked functionally graded rotor-bearing system using finite element analysis for the flexural vibrations. The functionally graded shaft is modelled using two nodded beam elements formulated using the Timoshenko beam theory. The flexibility matrix of a slant-cracked functionally graded shaft element has been derived using fracture mechanics concepts, which is further used to develop the stiffness matrix of a cracked element. Material properties are temperature and position-dependent and graded in a radial direction following power-law gradation. A Python code has been developed to carry out the complete finite element analysis to determine the Eigenvalues and Eigenvectors of a slant-cracked rotor subjected to different thermal gradients. The analysis investigates and further reveals significant effect of the power-law index and thermal gradients on the local flexibility coefficients of slant-cracked element and whirl natural frequencies of the cracked functionally graded rotor system.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

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