Over the past several decades, one class of problems in computational fluid dynamics (CFD) that has undergone substantial development involves movement of the fluid domain boundary. The problem class exists when the fluid domain boundary is either explicitly time-dependent, or is known a priori and determined as part of a flow solution in a coupled fashion. Free-surface fluid-structure interaction and forced-motion flows are typical of problems in this class. More specifically, as a boundary moves, a CFD mesh simulating the fluid dynamics can experience mesh cell distortion to the point of cell collapse, thereby rendering the CFD mesh meaningless.
A software module applicable to CFD was developed for 3D mesh updates when the domain boundary is moving and/or distorting. This robust method is especially useful for large motion/deformation situations in high Reynolds number simulations. The mesh movement algorithm is based on a modified form of the equilibrium equation governing classical linear elastostatics to coordinate the movement of mesh points within the computational domain in response to motion at the domain boundary.
To extend the method to large deformation and/or high Reynolds number flow regimes, two modifications are made to the known Navier equation and its finite volume discretization. The first modification stiffens mesh elements against shear distortion, and the second modification stiffens elements against size distortion in response to motion at the domain boundary. The first modification adds a source term to the known Navier equation; the second is implemented in the discrete form of the equation. In certain applications of the method, a novel near-wall node blanking procedure can also be applied. The near-wall blanking procedure overcomes a numerical conditioning problem that arises when slip boundary conditions are applied to the modified equilibrium equation at domain boundaries where high-aspect-ratio cells are used to resolve thin boundary layers.
An attractive feature of the mesh update method is that the equation governing linear elastostatics involves terms that are identical to terms in the compressible form of the Navier-Stokes equation governing the evolution of the flow. Consequently, the basic method can be readily implemented using an existing discretization of the Navier-Stokes equation as a template. This significantly reduces the development effort required by other methods. Furthermore, once the basic method has been implemented and evaluated, additional features of the method such as the rigid body rotation source term, slip boundary conditions, and high-aspect-ratio cell blanking may be implemented as needed.