Development of parallel meshless methods for moving geometry simulations

Computational uid dynamics methods to simulate ows around geometries in relative motion are important for the aerospace industry. Traditional methods like �nite-volume techniques are better suited for static simulations where the geometry of the problem does not change, or where only small movements are found. The meshless method can provide a solution for these problems where the geometry changes signi�cantly and di�erent bodies can move in relation to one another. A meshless method to select stencils from overlapping and moving point distributions, and a corresponding ow solver capable of solving the Euler equations on those stencils, have been developed previously. This work expands the existing meshless formulation by including the capabilities to simulate viscous ows in laminar and turbulent regimes and by implementing di�erent parallel computing techniques in an e�ort to improve the computational e�ciency. The treatment of viscous and turbulent ows is performed by augmenting the original Euler meshless scheme by using central-di�erences to discretise the viscous terms in the Navier-Stokes equations. The Spalart-Allmaras turbulence model is used to model the turbulent viscosity term and complete the closure of the system of equations to be solved. Validation of the method was carried out by calculating several well-known test cases and comparing the results to published data. The parallel implementation of the ow solver follows a distributed approach with asynchronous communications using message-passing standards. The parallel ow solver method is tested with two three-dimensional geometries, running in dedicated parallel machines with processor numbers ranging in the thousands. Results show good agreement to published data and very good parallel scalability. Preliminary testing of the stencil selection method, showed that the computational cost of the operations needed to �nd stencils for each point in the domain can vary dramatically for all points. Furthermore, this cost cannot be predicted a-priori, making it very di�cult to perform an appropriate domain decomposition. With this in mind, three types of implementation are used for the parallel stencil selection scheme: a distributed memory approach, a shared memory approach and hybrid method combining the two previous ones. Using the shared and hybrid implementations, the negative e�ects of using a poor domain decomposition are reduced. Four test cases are studied using the parallel stencil selection procedure coupled with the parallel ow solver. Two of these cases are static, and two of them are simulations over moving geometries. The fourth case introduces a 6 degree-of-freedom simulation to calculate the movement of a store being released from an aircraft and showcases the full capabilities of the method. These parallel tests show important reductions in the calculation times and open the door for the meshless scheme to be used in the future for more realistic cases