Towards a Unified Solution Method for Fluid-Structure Interaction Problems: Progress and Challenges

2006 ◽  
Author(s):  
G. Papadakis ◽  
C. G. Giannopapa
Keyword(s):  
Stress Tensor ◽  
Solution Method ◽  
Constitutive Relations ◽  
Fluid Structure Interaction ◽  
Strain Tensor ◽  
Internal Stresses ◽  
Fluid Structure ◽  
Structure Interaction ◽  
The Difference ◽  
Fundamental Equations

The paper presents the progress in the development of a novel unified method for solving coupled fluid-structure interaction problems as well as the associated major challenges. The new approach is based on the fact that there are four fundamental equations in continuum mechanics: the continuity equation and the three momentum equations that describe Newton’s second law in three directions. These equations are valid for fluids and solids, the difference being in the constitutive relations that provide the internal stresses in the momentum equations: in solids the stress tensor is a function of the strain tensor while in fluids the viscous stress tensor depends on the rate of strain tensor. The equations are written in such a way that both media have the same unknown variables, namely the three velocity components and pressure. The same discretisation technique (finite volume) and solution method (segregated approach) are used irrespective of the medium. Also the same methodology to handle the pressure-velocity coupling is employed. A common set of variables as well as a unified discretisation and solution method leads to a strong coupling between the two media and is very beneficial for the robustness of the algorithm. Significant challenges include the derivation of consistent boundary conditions for the pressure equation in boundaries with prescribed traction as well as the handling of discontinuity of pressure at the fluid-structure interface.

scholarly journals Indicative Results and Progress on the Development of the Unified Single Solution Method for Fluid-Structure Interaction Problems

2007 ◽  
Author(s):  
C. G. Giannopapa
Keyword(s):  
Solution Method ◽  
Numerical Models ◽  
Fluid Structure Interaction ◽  
Test Case ◽  
Computational Domain ◽  
Fluid Structure ◽  
Strongly Coupled ◽  
Structure Interaction ◽  
Fully Implicit ◽  
The Difference

This paper presents the progress on the development of a novel unified solution method for solving strongly coupled fluid-structure interaction problems. The method has been developed and fully tested for solids in [1]. The new approach is based on continuum mechanics formulation for fluids and structures where both continua can be solved using the momentum and continuity equation. The difference between the two continua lies in the constitutive equations. In this framework a single set of equations is used for the simultaneous solution of both fluid and solid. The common equations are written such that velocity and pressure are unknown variables for both continua. The discretisation method used for the solution of the problems is finite volumes. The physical interface between the two continua is treated as an internal part of the computational domain and no explicit exchange of information is needed. The test case used to demonstrate the idea is wave propagation in liquid filled flexible vessels. The solution is fully implicit and transient. Results regarding pressure, velocity and wall distention at different times and various locations along the tube are presented. The method is stable and robust and can be used for the next step of development and validation against classical analytical and numerical models.

scholarly journals Linear Stability Analysis and Validation of a Unified Solution Method for Fluid-Structure-Interaction on Structural Dynamic Problems

2005 ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Structural Dynamic ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: Partitioned methods and monolithic methods. Both methods use two separate sets of equations for fluid and solid. A unified solution method has been presented [1], which is different from these methods. The new method treats both fluid and solid as a single continuum, thus the whole computational domain is treated as one entity discretised on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, 2 time marching and one spatial discretisation scheme, widely used for fluids’ equations, are applied for the solution of the equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps and beam sizes is also presented. For all cases examined the numerical solution was stable and robust and proved to be suitable for the next stage of application to full fluid-structure interaction problems.

Linear Stability Analysis and Application of a New Solution Method of the Elastodynamic Equations Suitable for a Unified Fluid-Structure-Interaction Approach

2008 ◽  
Vol 130 (3) ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Solution Method ◽  
Stokes Equations ◽  
Fluid Structure Interaction ◽  
Analytic Solutions ◽  
Computational Domain ◽  
Fluid Structure ◽  
Structure Interaction

In the conventional approach for fluid-structure-interaction problems, the fluid and solid components are treated separately and information is exchanged across their interface. According to the conventional terminology, the current numerical methods can be grouped in two major categories: partitioned methods and monolithic methods. Both methods use separate sets of equations for fluid and solid that have different unknown variables. A unified solution method has been presented in the previous work of Giannopapa and Papadakis (2004, “A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems,” ASME PVP 2004, San Diego, CA, July, PVP Vol. 491–1, pp. 111–117), which is different from these methods. The new approach treats both fluid and solid as a single continuum; thus, the whole computational domain is treated as one entity discretized on a single grid. Its behavior is described by a single set of equations, which are solved fully implicitly. In this paper, the elastodynamic equations are reformulated so that they contain the same unknowns as the Navier–Stokes equations, namely, velocities and pressure. Two time marching and one spatial discretization scheme, widely used for fluid equations, are applied for the solution of the reformulated equations for solids. Using linear stability analysis, the accuracy and dissipation characteristics of the resulting difference equations are examined. The aforementioned schemes are applied to a transient structural problem (beam bending) and the results compare favorably with available analytic solutions and are consistent with the conclusions of the stability analysis. A parametric investigation using different meshes, time steps, and beam dimensions is also presented. For all cases examined, the numerical solution was stable and robust and therefore is suitable for the next stage of application to full fluid-structure-interaction problems.

Fluid-structure interaction simulations for a temperature-sensitive functionally graded hydrogel-based micro-channel

2020 ◽  
pp. 1045389X2096317
Author(s):  
Amir Ghasemkhani ◽  
Hashem Mazaheri ◽  
Arya Amiri
Keyword(s):  
Fluid Structure Interaction ◽  
Vital Role ◽  
Functionally Graded ◽  
Temperature Sensitive ◽  
Micro Channel ◽  
Exponential Form ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Number Of Layers ◽  
The Difference

The behavior of a temperature-sensitive micro-channel have been investigated in this study which mainly includes a functionally graded (FG) hydrogel as a sensor or an actuator. In order to achieve this goal, both fluid-structure interaction (FSI) and non-FSI simulations are conducted for hydrogel with homogeneous property distribution as well as FG hydrogels with different number of layers (2–16 layers). Moreover, this study investigates the FG hydrogel cross-linking density that obeys a general exponential form. In addition to all mentioned, the FG hydrogels are considered in both ascending and descending states with vertically and horizontally functionally graded property distributions (VFG and HFG hydrogels). Subsequently, the importance of the difference between the FG and homogenous hydrogels has been highlighted in the findings of the study. Besides, the FSI influence has a vital role in these structures especially once an FG material is utilized. According to the findings, the ascending and descending distributions of the hydrogel properties may significantly affect the micro-channel behavior, especially in horizontally graded type. This process can be done in a way that for descending distribution of HFG there exist no closing state for the micro-channel.

A New Formulation for Solids Suitable for a Unified Solution Method for Fluid-Structure Interaction Problems

2004 ◽  
Author(s):  
C. G. Giannopapa ◽  
G. Papadakis
Keyword(s):  
Solution Method ◽  
Fluid Structure Interaction ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Stage Of Development ◽  
Cantilevered Beam ◽  
New Formulation ◽  
Development And Validation ◽  
Velocity Pressure ◽  
Single Set

In fluid-structure interaction problems, the fluid and solid components are solved separately and information is exchanged along the interface. This work shows the first stage of development and validation of a novel unified solution method suitable for computing fluid-structure interaction problems. In the new method, a single set of equations is used to describe both fluid and solid, while the interface between them is contained within the solution domain itself. This can be achieved by reformulating the solid equations to solve for the same primitive variables used in fluids i.e. velocity and pressure. The PISO algorithm is used to handle the velocity-pressure coupling. Although this is a standard approach for fluids, validation is needed for solids. Two cases are examined: wave propagation in a one-dimensional rod and oscillation of a 2D cantilevered beam. Appropriate set of boundary conditions is chosen for the free surface. The new formulation for solids is stable and robust, thus it can be used in the next stage in the development of a robust algorithm for coupled fluid-structure interaction problems.

Characterization of Polymeric Membranes Under Large Deformations Using Fluid-Structure Coupling

2015 ◽  
Vol 07 (05) ◽  
pp. 1550068 ◽  
Author(s):  
Fouad Erchiqui ◽  
Mhamed Souli ◽  
Toufik Kanit ◽  
Abdellatif Imad ◽  
Boudlal Aziz ◽  
...  
Keyword(s):  
Fluid Structure Interaction ◽  
Acrylonitrile Butadiene Styrene ◽  
Arbitrary Lagrangian Eulerian ◽  
Ann Model ◽  
Equilibrium Equations ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Gas Dynamic ◽  
The Difference ◽  
Artificial Neural Network Ann

The mechanical properties of Ogden material under biaxial deformation are obtained by using the bubble inflation technique. First, pressure inside the bubble and height at the hemispheric pole are recorded during bubble inflation experiment. Thereafter, Ogden's theory of hyperelasticity is employed to define the constitutive model of flat circular thermoplastic membranes (CTPMs) and nonlinear equilibrium equations of the inflation process are solved using finite difference method with deferred corrections. As a last step, a neuronal algorithm artificial neural network (ANN) model is employed to minimize the difference between calculated and measured parameters to determine material constants for Ogden model. This technique was successfully implemented for acrylonitrile-butadiene-styrene (ABS), at typical thermoforming temperatures, 145°C. When solving for the bubble inflation, the recorded pressure is applied uniformly on the structure. During the process inflation, the pressure is not uniform inside the bubble, thus full gas dynamic equations need to be solved to get the appropriate nonuniform pressure to be applied on the structure. In order to simulate the inflation process accurately, computational fluid dynamics in a moving fluid domain as well as fluid structure interaction (FSI) algorithms need to be performed for accurate pressure prediction and fluid structure interface coupling. Fluid structure interaction solver is then required to couple the dynamic of the inflated gas to structure motion. Recent development has been performed for the simulation of gas dynamic in a moving domain using arbitrary Lagrangian Eulerian (ALE) techniques.

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