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

Abstract

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.

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

“…The percentage difference between the analytical and the numerical solution is 2.05 % for the frequency and 9.21% for the displacement (Table 2). More results can be found in references [9,10,11].…”

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

“…In order to investigate the numerical dissipation of the two methods, a calculation was performed until time t=100s. In a previous study [1], it was found that the standard stress analysis completely dissipates after 56 beam oscillations, whereas the velocity formulation has dissipated 33% after 332 oscillations. The reason for this behavior can now be explained from the conclusions of linear stability analysis presented earlier on.…”

“…The single solution method [1,7] used in this paper is a fully coupled method in which the fluid and solid are solved simultaneously for each time step in a single solution domain ( Figure 1c). A single set of equations is used to describe the fluid and solid and their interface is contained within the solution domain itself making the coupling inherently implicit.…”

“…This paragraph is concerned with the presentation of the mathematical formulation of the unified method for the solution of the equations for solids and liquids as described in [1,7]. The resulting set of equations contains the three velocity components and pressure as unknown variables.…”

“…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.…”