scholarly journals On the effect of the bulk tangent matrix in partitioned solution schemes for nearly incompressible fluids

2014 ◽  
Vol 102 (3-4) ◽  
pp. 257-277 ◽  
Author(s):  
Alessandro Franci ◽  
Eugenio Oñate ◽  
Josep Maria Carbonell
Keyword(s):  
Incompressible Fluids ◽  
Tangent Matrix

The Propagation of Shock Waves in Incompressible Fluids: The Case of Freshwater

2014 ◽  
Vol 132 (1) ◽  
pp. 427-437 ◽  
Author(s):  
Andrea Mentrelli ◽  
Tommaso Ruggeri
Keyword(s):  
Shock Waves ◽  
Incompressible Fluids

ON THE APPLICATION OF A NOVEL ALGORITHM TO HYDRODYNAMIC DIFFUSION AND VELOCITY FLUCTUATIONS IN SEDIMENTING SYSTEMS

1996 ◽  
Vol 07 (04) ◽  
pp. 543-561 ◽  
Author(s):  
WOLFGANG KALTHOFF ◽  
STEFAN SCHWARZER ◽  
GERALD RISTOW ◽  
HANS J. HERRMANN
Keyword(s):  
Numerical Simulations ◽  
Numerical Method ◽  
Incompressible Fluids ◽  
Strong Anisotropy ◽  
Velocity Fluctuations ◽  
Drag Forces ◽  
Large Numbers ◽  
Spatial Dimensions ◽  
Experimental Findings ◽  
Novel Algorithm

We present a numerical method to deal efficiently with large numbers of particles in incompressible fluids. The interactions between particles and fluid are taken into account by a physically motivated ansatz based on locally defined drag forces. We demonstrate the validity of our approach by performing numerical simulations of sedimenting non-Brownian spheres in two spatial dimensions and compare our results with experiments. Our method reproduces qualitatively important aspects of the experimental findings, in particular the strong anisotropy of the hydrodynamic bulk self-diffusivities.

scholarly journals Numerical Algorithms for Elastoplacity: Finite Elements Code Development and Implementation of the Mohr–Coulomb Law

2021 ◽  
Vol 11 (10) ◽  
pp. 4637
Author(s):  
Gildas Yaovi Amouzou ◽  
Azzeddine Soulaïmani
Keyword(s):  
Fixed Point ◽  
Finite Difference ◽  
Difference Scheme ◽  
Finite Difference Scheme ◽  
Numerical Algorithms ◽  
Constitutive Law ◽  
Layer By Layer ◽  
Implementation Framework ◽  
Fixed Point Algorithm ◽  
Tangent Matrix

Two numerical algorithms for solving elastoplastic problems with the finite element method are presented. The first deals with the implementation of the return mapping algorithm and is based on a fixed-point algorithm. This method rewrites the system of elastoplasticity non-linear equations in a form adapted to the fixed-point method. The second algorithm relates to the computation of the elastoplastic consistent tangent matrix using a simple finite difference scheme. A first validation is performed on a nonlinear bar problem. The results obtained show that both numerical algorithms are very efficient and yield the exact solution. The proposed algorithms are applied to a two-dimensional rockfill dam loaded in plane strain. The elastoplastic tangent matrix is calculated by using the finite difference scheme for Mohr–Coulomb’s constitutive law. The results obtained with the developed algorithms are very close to those obtained via the commercial software PLAXIS. It should be noted that the algorithm’s code, developed under the Matlab environment, offers the possibility of modeling the construction phases (i.e., building layer by layer) by activating the different layers according to the imposed loading. This algorithmic and implementation framework allows to easily integrate other laws of nonlinear behaviors, including the Hardening Soil Model.

scholarly journals Lagrangian controllability of inviscid incompressible fluids: a constructive approach

2017 ◽  
Vol 23 (3) ◽  
pp. 1179-1200
Author(s):  
Thierry Horsin ◽  
Otared Kavian
Keyword(s):  
Numerical Simulations ◽  
Euler Equation ◽  
Approximate Controllability ◽  
Holomorphic Functions ◽  
Rational Functions ◽  
Incompressible Fluids ◽  
Constructive Method ◽  
Constructive Approach ◽  
Density Result

We present here a constructive method of Lagrangian approximate controllability for the Euler equation. We emphasize on different options that could be used for numerical recipes: either, in the case of a bi-dimensionnal fluid, the use of formal computations in the framework of explicit Runge approximations of holomorphic functions by rational functions, or an approach based on the study of the range of an operator by showing a density result. For this last insight in view of numerical simulations in progress, we analyze through a simplified problem the observed instabilities.

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