tions, with due care taken to account for the discontinuities in the interaction flow. The convective difference scheme, A method of second-order accuracy is described for integrating the equations of ideal compressible flow. The method is based on hidden in the Lagrangean scheme, for integrating the charthe integral conservation laws and is dissipative, so that it can be acteristic equations is a so-called up-stream-centered (upused across shocks. The heart of the method is a one-dimensional wind) scheme and has been discussed as ''scheme II'' in Lagrangean scheme that may be regarded as a second-order sequel the previous paper [2] of this series. Remapping the Lato Godunov's method. The second-order accuracy is achieved by grangean results onto an Euler grid is done according to taking the distributions of the state quantities inside a gas slab to be linear, rather than uniform as in Godunov's method. The the upstream-centered ''scheme III'' from the same paper. Lagrangean results are remapped with least-squares accuracy onto A substantial improvement will still result if, in the Lathe desired Euler grid in a separate step. Several monotonicity algograngean step, scheme II is replaced by the more accurate rithms are applied to ensure positivity, monotonicity, and nonlinear scheme III.
stability. Higher dimensions are covered through time splitting. Nu-An accessory technique for preserving monotonicity merical results for one-dimensional and two-dimensional flows are presented, demonstrating the efficiency of the method. The paper during convection, also discussed in [2], is easily incorpoconcludes with a summary of the results of the whole series ''Torated in the method. It is applied in its crudest form [2, wards the Ultimate Conservative Difference Scheme.'' แฎ 1979 Aca-Eq. ( 66)] at the beginning of the Lagrangean step; a more demic Press sophisticated form [2, Eq. ( 74)] is applied in the remap step. Further refinement of the technique has been projected.
Numerical experiments indicate that for solving two-