scholarly journals A conservative finite element method for the incompressible Euler equations with variable density

2020 ◽  
Vol 412 ◽  
pp. 109439 ◽  
Author(s):  
Evan S. Gawlik ◽  
François Gay-Balmaz
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Euler Equations ◽  
Variable Density ◽  
Incompressible Euler Equations ◽  
Incompressible Euler ◽  
Element Method

scholarly journals Error analysis of a fully discrete finite element method for incompressible flow with variable density

2020 ◽  
Author(s):  
Wentao Cai ◽  
Buyang Li ◽  
Ying Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Incompressible Flow ◽  
Stokes Equations ◽  
Coupled System ◽  
Variable Density ◽  
Spatial Error ◽  
Fully Discrete ◽  
Stabilized Finite Element Method ◽  
Element Method

An error estimate is presented for a fully discrete, linearized and stabilized finite element method for solving the coupled system of nonlinear hyperbolic and parabolic equations describing incompressible flow with variable density. In particular, the error of the numerical solution is split into the temporal and spatial components, separately. The temporal error is estimated by applying discrete maximal L^p-regularity of time-dependent Stokes equations, and the spatial error is estimated by using energy techniques based on the uniform regularity of the solutions given by semi-discretization in time.

Topological Optimization Design for Pedestal of Horizontal Rocket Rivet Fixture

2011 ◽  
Vol 291-294 ◽  
pp. 2601-2607
Author(s):  
Zhou Yang Li ◽  
Wen Tao Gu ◽  
Ming Jun Wang ◽  
Yan Ni Lei
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Stress Distribution ◽  
Optimization Design ◽  
Variable Density ◽  
Topological Optimization ◽  
The Finite Element Method ◽  
Guide Rail ◽  
Set Up ◽  
Element Method

In order to improve the riveting precision, the finite element method and topological optimization design based on the variable density method were employed to design the pedestal of horizontal rocket rivet fixture. Topological optimization model was set up based on static analysis of the original designed pedestal under various typical load cases. Topological optimization results of various load cases were compared with original pedestal. The result showed deficiencies of the original pedestal, and a new model was built based on topological optimization results. The analysis of topological model was carried out by applying the finite element method. The results show that the stiffness of pedestal was remarkably improved; the stress distribution was more homogenized and the displacement of the guide rail was decreased after optimization. This method could also provide reference and guidance for designing other complicated structures.

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