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Full-Text Articles in Mechanical Engineering
Optimum Grid By Direct Optimization Methods, Ajay Mahajan, Richard Hindman
Optimum Grid By Direct Optimization Methods, Ajay Mahajan, Richard Hindman
Dr. Ajay Mahajan
A solution-adaptive grid procedure based on optimization is developed and applied to the Linearized Viscous Burger's governing equation. The scheme redistributes the grid points as the solution adapts through each successive iteration step to minimize the truncation error terms in the modified equation and satisfy the governing equation. Fist order Roe scheme is used to discretize the governing equation. If the truncation error terms become negligible and the governing equation is satisfied by the scheme then the numerical solution approaches the exact solution.
Grid And Solution Adaptation Via Direct Optimization Methods, Ajay Mahajan
Grid And Solution Adaptation Via Direct Optimization Methods, Ajay Mahajan
Dr. Ajay Mahajan
At present all numerical schemes based on some form of differencing approach are plagued by some lack of accuracy when compared to the exact solution. This lack of accuracy can be attributed to the presence of truncation error in the numerical method. Traditionally the error can be reduced by increasing the number of mesh points in the discrete domain or by implementing a higher order numerical scheme. In recent times the approach has taken a more intelligent direction where adaptation or distribution of the mesh points is affected in such a way to reduce the error. However, grid adaptation with …