Finite Difference Calculations
1 Dimensional Advection
LL Takacs - Mon. Wea. Rev. (1985) 113 (6): 1050–1065. journals.ametsoc.org.
A two-step advection scheme of the Lax-Wendroff type is derived which has accuracy and phase characteristics similar to that of a third-order scheme. The scheme is exactly third-order accurate in time and space for uniform flow. The new scheme is compared with other currently used methods, and is shown to simulate well the advection of localized disturbances with steep gradients. The scheme is derived for constant flow and generalized to two-dimensional nonuniform flow.
MacCormack, R. W., The Effect of viscosity in hypervelocity impact cratering, AIAA Paper, 69-354 (1969).
A numerical method, of second order in both time and space, for the solution of the time-dependent compressible Navier-Stokes equations is presented. Conditions for stability are discussed. The method has been applied to calculate an axisymmetric flow field produced by hypervelocity impact. Results are given for impacts of aluminum cylinders (having diameters of 0.16, 0.32, and 0.64 cm) into aluminum targets. Viscosities of zero and 104 poise were assumed.
Takacs scheme using Java programming language.
