In this paper, based on the boundary approximation approach for parallelization of the compact difference schemes, a novel strategy for the sub-domain boundary approximation schemes is proposed to maintain consistent accuracy and dispersion with the compact scheme in the interior points. In this strategy, not only the order of accuracy of the sub-domain boundary scheme is the same as the interior scheme, but the coefficient of the first truncation error term is also equal to that of the internal scheme. Furthermore, to realize the consistent dispersion performance for a class of high order upwind compact schemes, which usually include two expressions, we modify the opposite expression to be the sub-domain boundary scheme. As an example of application, the present strategy is applied to a fourth-order upwind compact scheme, and its accuracy is verified by a numerical test. The resolution and efficiency of the newly proposed parallel method are examined by four numerical examples, including propagation of a wave-packet, convection of isentropic vortex, Rayleigh–Taylor instability problems, and propagation of Gauss pulse. The results obtained demonstrate that the present strategy for compact difference schemes has the feasibility to solve the flow problems with high accuracy, resolution and efficiency in parallel computation.

本文基于紧致差分方案并行化的边界近似方法，提出了一种新的子域边界近似方案策略，以保持与紧致方案在内部点的一致精度和分散性。在该策略中，不仅子域边界方案的精度顺序与内部方案相同，而且第一截断误差项的系数也等于内部方案。此外，为了实现一类通常包含两个表达式的高阶迎风紧凑方案的一致分散性能，我们将相反的表达式修改为子域边界方案。作为应用示例，本策略适用于四阶迎风紧凑方案，并通过数值测试验证了其准确性。通过四个数值示例检验了新提出的并行方法的分辨率和效率，其中包括波包的传播，等熵涡旋对流，瑞利-泰勒不稳定性问题以及高斯脉冲的传播。所得结果表明，该紧凑差分方案的策略具有可行性，可以在并行计算中以高精度，高分辨率和高效率解决流动问题。