On the development of a meshless method to study multibody systems using computational fluid dynamics

摘要

Multibody systems, which consist of several separate or interconnected, rigid or flexible bodies, occur frequently in problems of aerospace engineering. Such problems can be difficult to solve using conventional finite volume methods in computational fluid dynamics. This is particularly so if the bodies are required to undergo translational or rotational displacements during time-dependent simulations, which occur, for example, with cases involving store release or control surface deflection. These problems are generally limited to those when the movements are small or known a-priori. This thesis investigates the use of the meshless method to solve these difficult multibody systems using computational fluid dynamics, with the aim of performing moving-body simulations involving large scale motions, with no restrictions on the movement. An implicit meshless scheme is developed to solve the Euler, laminar and Reynolds-Averaged Navier-Stokes equations. Spatial derivatives are approximated using a least squares method on clouds of points. The resultant system of equations is linearised and solved implicitly using approximate, analytical Jacobian matrices and a preconditioned Krylov subspace iterative method. The details of the spatial discretisation, linear solver and construction of the Jacobian matrix are discussed, and results which demonstrate the performance of the scheme are presented for steady and unsteady flows in two and three-dimensions. The selection of the stencils over the computational domain for the meshless solver is vital for the method to be used to solve problems involving multibody systems accurately and efficiently. The computational domain is obtained using overlapping point distributions associated with each body in the system. Stencil selection is relatively straight forward if the point distributions are isotropic in nature; however, this is rarely the case in computations that solve the Navier-Stokes equations. A fully automatic method of selecting the stencils is outlined, in which the original connectivity and the concept of a resolving direction are used to help construct good quality stencils with limited user input. The methodology is described, and results, that are solutions to the Navier-Stokes equations in two-dimensions and the Euler equations in three-dimensions, are presented for various systems.