CARTESIAN GRID SOLUTION OF THE EULER EQUATIONS USING A GRIDLESS BOUNDARY CONDITION TREATMENT

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 multi- grid 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.

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