A Two-Grid Technique for the Penalty Method of the Steady Navier-Stokes Equations

A two grid technique for solving the steady incompressible Navier Stokes equations in a penalty method was presented and the convergence of numerical solutions was analyzed. If a coarse size H and a fine size h satisfy H=O(h 13-s )(s=0(n=2);s=12(n=3), where n is a space dimension), this method has the same convergence accuracy as the usual finite element method. But the two grid method can save a lot of computation time for its brief calculation. Moreover, a numerical test was couducted in order to verify the correctness of above theoretical analysis.

Preconditioned method in parallel computation

The grid equations in decomposed domain by parallel computation are soled, and a method of local orthogonalization to solve the large-scaled numerical computation is presented. It constructs preconditioned iteration matrix by the combination of predigesting LU decomposition and local orthogonalization, and the convergence of solution is proved. Indicated from the example, this algorithm can increase the rate of computation efficiently and it is quite stable.

Smolyak Type Sparse Grid Collocation Method for Uncertainty Quantification of Nonlinear Stochastic Dynamic Equations

This paper develops a Smolyak-type sparse-grid stochastic collocation method(SGSCM) for uncertainty quantification of nonlinear stochastic dynamic equations.The solution obtained by the method is a linear combination of tensor product formulas for multivariate polynomial interpolation.By choosing the collocation point sets to coincide with cubature point sets of quadrature rules,we derive quadrature formulas to estimate the expectations of the solution.The method does not suffer from the curse of dimensionality in the sense that the computational cost does not increase exponentially with the number of input random variables.Numerical analysis of a nonlinear elastic oscillator subjected to a discretized band-limited white noise process demonstrates the computational efficiency and accuracy of the developed method.

A fast and automatic full-potential finite volume solver on Cartesian grids for unconventional configurations

To meet the requirements of fast and automatic computation of subsonic and transonic aerodynamics in aircraft conceptual design,a novel finite volume solver for full potential flows on adaptive Cartesian grids is developed in this paper.Cartesian grids with geometric adaptation are firstly generated automatically with boundary cells processed by cell-cutting and cell-merging algorithms.The nonlinear full potential equation is discretized by a finite volume scheme on these Cartesian grids and iteratively solved in an implicit fashion with a generalized minimum residual（GMRES） algorithm.During computation,solution-based mesh adaptation is also applied so as to capture flow features more accurately.An improved ghost-cell method is proposed to implement the non-penetration wall boundary condition where the velocity-potential of a ghost cell is modified by an analytic method instead.According to the characteristics of the Cartesian grids,the Kutta condition is applied by specially computing the gradients on Kutta-faces without directly assigning the potential jump to cells adjacent wake faces,which can significantly improve the solution converging speed.The feasibility and accuracy of the proposed method are validated by several typical cases of sub/transonic flows around an ONERA M6 wing,a DLR-F4 wing-body,and an unconventional figuration of a blended wing body（BWB）.The validation cases demonstrate a fast convergence with fully automatic grid treatment and computation,and the results suggest its capacity in application for aircraft conceptual design.