## 6 Mechanical Systems--Case Study Application
### Moving Zones--CFD Application  
The CFD technique has been broadly used in the last fifty years for the fluid and fluid-structure interaction problems. Predictions of the fluid motions around structures along with the pressure wave generated by moving objects are crucial for the design of engineering systems (fluid-structure problem) in many branches of engineering. Until recent decades, only the wind tunnel and full-scale field studies could represent the service life conditions for the fluid-structure interactions and fluid dynamics around large structures. However, with the rapid developments of advanced numerical techniques, including the expansion of computational power and parallelization, sophisticated pre- and post-processing capabilities, and more efficient algorithms, CFD becomes a viable tool for making numerical simulations of complex geometric fluid-structure interaction problems. Large space structures like road/rail gantries may be subject to vibrational resonance owing to aerodynamic effects from environmental wind (gust effects) and/or HSV buffeting. In addition to ultimate strength and static/dynamic forces considered for the design of these vital structures, there are also other dynamic effects like fatigue service life that need to be considered in the design. These dynamic considerations can be characterized into two major effects: firstly, it can induce significant fatigue effects through large cyclic stresses, which have to be considered to avoid premature fatigue failures during expected life; secondly, it can have excessive vibrational effects and resonance (flexural and torsional), which can either cause structural and equipment damages or prevent/reduce their service functionalities. The simulations of moving objects/zones within numerical domains that include fluid and solid boundaries have always been a challenging task among scientist and practicing engineers. The motion of a virtual vehicle under a solid/flexible gantry model needs to be accurately modeled to generate an appropriate dynamic pressure wave for the design. Some early aspects of the advanced zoning technique have been developed recently to overcome numerical problems related to continuous motion/generation of objects within a numerical domain [19]. The dynamic nature of the numerical domain in these simulations has conventionally been ignored or modelled through some pseudo-static techniques. However, using the efficient interfacing technology and the advance grid to grid interface,the movement of the vehicle zone against the stationary gantry zone (within the main atmospheric domain) can be simulated for road/rail structure application. The standard formulation for the conservation of the variable (\(\phi\)) for a control volume \(V\) with moving boundaries is [33; 34; 35; 36]  
\[\frac{d}{dt}\int_{V}\rho\varphi dV+\int_{\partial V}\rho\varphi\big{(}u-u_{g} \big{)}.dA=\int_{\partial V}\Gamma\
abla\varphi\cdot dA+\int_{V}S_{\varphi}dV \tag{42}\]  
where \(\rho\) and \(u\) are the fluid density and velocity, respectively, and \(u_{g}\) is the velocity of moving interface. The time varying conservation term in Equation (42) can be numerically calculated using the backward difference method as  
\[\frac{d}{dt}\int_{V}\rho\varphi dV=\frac{\left(\rho\varphi V\right)^{n+1}-\left( \rho\varphi V\right)^{n}}{\Delta t} \tag{43}\]  
and the change in the control volume during the simulation can also be written as  
\[V^{n+1}=V^{n}+\frac{dV}{dt}\Delta t=V^{n}+(\int_{\partial V}u_{g}\cdot dA) \Delta t=V^{n}+(\sum_{j}^{f}u_{g,j}A_{j})\Delta t \tag{44}\]  
where \(A_{j}\) is the face area vector and \(f\) is the number of faces on the control volume. More comprehensive discussions about the conventional moving mesh theory can be found in [36; 37]. Among dynamic mesh methods, the moving finite volume method [10; 18] and the moving finite difference method have attracted considerable interest for dynamic simulation in recent years.