A Conservative Second-Order Accurate Fluid Algorithm for Variable Spatial Grid.
NAVAL RESEARCH LAB WASHINGTON D C
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The widely used Lax-Wendroff two-step algorithm for solving fluid equations is well known to be conservative and second order accurate on a constant spatial grid. But on a variable grid the accuracy is reduced to first order although the conservative property remains. A modification of this method is introduced which is both conservative and second order accurate on the variable grid. This method works well with all of the fluid equations but the author examines the simplest case and studies the continuity equation with a constant velocity field. For a given Fourier mode the amplitude and phase errors are obtained in the three dimensional parameter space of wavelength, fluid speed, and grid spacing ratio. A test problem is run with each of the algorithms and the errors are followed as a function of time. All of the results confirm our expectation that the modified algorithm is significantly more accurate in regions where the grid is variable and indeed is second order accurate there. Author
- Theoretical Mathematics
- Fluid Mechanics