scholarly journals Parallel time-stepping for fluid-structure interactions

2021 ◽  
Author(s):  
Thomas Richter ◽  
Nils Margenberg
Keyword(s):  
Stokes Equations ◽  
Numerical Test ◽  
Time Integration ◽  
Navier Stokes ◽  
Fluid Structure Interactions ◽  
Fluid Structure ◽  
Solution Approach ◽  
Time Stepping ◽  
Parallel Time ◽  
Nicolson Scheme

We present a parallel time-stepping method for fluid-structure   interactions. The interaction between the incompressible   Navier-Stokes equations and a hyperelastic solid is formulated in a   fully monolithic framework. Discretization in space is based on   equal order finite element for all variables and a variant of the   Crank-Nicolson scheme is used as second order time integrator. To   accelerate the solution of the systems, we analyze a parallel-in   time method. For different numerical test cases in 2d and in 3d we   present the efficiency of the resulting solution approach. We also   discuss some challenges and limitations that are connected   to the special structure of fluid-structure interaction problem.   In particular, we will investigate stability and dissipation     effects of the time integration and their influence on the     convergence of the Parareal method. It turns out that especially     processes based on an internal dynamics (e.g. driven by the vortex     street around an elastic obstacle) cause great     difficulties. Configurations however, which are driven by     oscillatory problem data, are well-suited for parallel time     stepping and allow for substantial speedups.

scholarly journals A natural element updated Lagrangian approach for modelling fluid structure interactions

2007 ◽  
pp. 323-336
Author(s):  
Andrés Galavís ◽  
David González ◽  
Elias Cueto ◽  
Francisco Chinesta ◽  
Manuel Doblaré
Keyword(s):  
Stokes Equations ◽  
Theoretical Description ◽  
Navier Stokes ◽  
Fluid Structure Interactions ◽  
Navier Stokes Equations ◽  
Fluid Structure ◽  
Lagrangian Framework ◽  
Natural Element ◽  
Updated Lagrangian Approach ◽  
Updated Lagrangian

In this paper we present a novel methodology for the numerical simulation of fluid structure interactions in the presence of free surfaces. It is based on the use of the Natural Element Method (NEM) in an updated Lagrangian framework, together with the integration of the Navier-Stokes equations by employing a Galerkin-characteristics formulation. Tracking of the free-surface is made by employing shape constructors, in particular α- shapes. A theoretical description of the method is made and also some examples of the performance of the technique are included.

Simulation of the Transitional Flow in a Low Pressure Gas Turbine Cascade With a High-Order Discontinuous Galerkin Method

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
A. Ghidoni ◽  
A. Colombo ◽  
S. Rebay ◽  
F. Bassi
Keyword(s):  
Discontinuous Galerkin ◽  
Turbulence Model ◽  
Stokes Equations ◽  
Time Integration ◽  
High Order ◽  
Transitional Flow ◽  
Navier Stokes ◽  
Implicit Time ◽  
Turbine Cascade ◽  
High Reynolds

In the last decade, discontinuous Galerkin (DG) methods have been the subject of extensive research efforts because of their excellent performance in the high-order accurate discretization of advection-diffusion problems on general unstructured grids, and are nowadays finding use in several different applications. In this paper, the potential offered by a high-order accurate DG space discretization method with implicit time integration for the solution of the Reynolds-averaged Navier–Stokes equations coupled with the k-ω turbulence model is investigated in the numerical simulation of the turbulent flow through the well-known T106A turbine cascade. The numerical results demonstrate that, by exploiting high order accurate DG schemes, it is possible to compute accurate simulations of this flow on very coarse grids, with both the high-Reynolds and low-Reynolds number versions of the k-ω turbulence model.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals Choice and Limits of a Fluid Model for the Numerical Study in Dynamic Fluid Structure Interaction Problems

2003 ◽  
Author(s):  
Jean Franc¸ois Sigrist ◽  
Christian Laine ◽  
Dominique Lemoine ◽  
Bernard Peseux
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Model ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Linear Solution ◽  
Fluid Structure ◽  
Design Engineers ◽  
Inviscid Incompressible Fluid ◽  
Basic Fluid

This paper is related to the study of a nuclear propulsion reactor prototype for the French Navy. This prototype is built on ground and is to be dimensioned toward seismic loading. The dynamic analysis takes the coupled fluid structure analysis into account. The basic fluid models used by design engineers are inviscid incompressible or compressible. The fluid can be described in a bidimensional by slice or a three-dimensional approach. A numerical study is carried out on a generic problem for the linear FSI dynamic problem. The results of this study are presented and discussed. As a conclusion, the three-dimensional inviscid incompressible fluid appears to be the best compromise between the description of physical phenomena and the cost of modeling. The geometry of the reactor is such that large displacements of the structure in the fluid can occur. Therefore, the linearity hypothesis might not be longer valid. The case of large amplitude imposed oscillating motion of a cylinder in a confined fluid is numerically studied. A CFD code is used to investigate the fluid behavior solving the NAVIER-STOKES equations. The forces induced on the cylinder by the fluid are computed and compared to the linear solution. The limit of the linear model can then be exhibited.

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