The convergence properties of a patched Cartesian field mesh using a gridless boundary condition treatment are presented in the solution of the Euler equations for transonic flow. The gridless treatment employs a least squares fitting of the conserved flux variables using a cloud of nodes in the vicinity of the body in order apply requisite surface boundary conditions. Various multi-grid acceleration strategies are discussed for both single and dual NACA 0012 airfoil configurations. Results show that multigrid acceleration can provide a substantial decrease in computational work indicating a significant advantage over purely gridless schemes in which efficient implementation of multi-grid is problematic. Additionally, an enhanced treatment of the trailing edge discretization is presented in which issues associated with thin body geometry are alleviated, establishing an advantage over other Cartesian mesh methodologies. Comparisons to results incorporating a body-fitted mesh are also provided to establish the accuracy of the method. Finally, solution invariance is established for cases in which the body is not directly aligned with the Cartesian mesh establishing the flexibility of the method.
A numerical method for the treatment of boundary conditions in non-body conforming computational grids is proposed.The method incorporates a "gridless" algorithm in which numerical boundary conditions may be imposed in such a manner that explicit connectivity between surface geometry and field mesh is not required. As a result, solutions to problems in computational physics are greatly facilitated since definition of the body geometry may be generated independently from the field mesh. Furthermore, perturbations in body geometry may be introduced into the simulation without the requirement for regeneration of the field mesh (i.e. wing flap deflection). The method is particularly suited for Cartesian mesh applications, in which convergence and stability issues associated with mesh skewness and distortion are eliminated. Furthermore, the method does not require special treatment for "thin body" problems from which many Cartesian methodologies suffer. The applicability of the method for two-dimensional Euler simulations with examples of transonic flow over a NACA 0012 airfoil is presented here. Results of the method are shown to compare very favorably with traditional body-fitted mesh techniques.
A method for the prediction of transonic flutter by the Euler equations on a Cartesian mesh is presented. Surface boundary conditions are applied using a perturbation of a gridless treatment in such a manner that solutions are obtained on a stationary mesh. For steady problems, the gridless method applies surface boundary conditions using a weighted average of the flow properties within a cloud of nodes in the vicinity of the surface. Weight functions are derived based on a least squares fitting of the surrounding cloud of nodes.For unsteady calculations, a perturbation of the weight functions is incorporated to account for a fluctuating surface normal direction. Additionally, a varying surface normal velocity is introduced into the boundary treatment. The nature of the method provides for efficient and accurate solution of transient problems in which surface deflections are small (i.e. flutter calculations) without the need for a deforming mesh. Problem setup also requires minimal effort due to the use of patched embedded Cartesian grids. Although deviations in the airfoil angle of attack are small, the mean angle of attack can be large, being prescribed by the far field boundary condition. Results show good agreement with available experimental data and wing flutter computations using traditional moving mesh algorithms considering a two-degree of freedom structural wing model.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.