Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. In the fourth paper, the application of the Fourier series multiscale method to the one- and two-dimensional convection-diffusion-reaction equations is implemented, where the Fourier series multiscale solutions are derived, the convergence characteristics of the Fourier series multiscale solutions are investigated by numerical examples, the schemes for application of the Fourier series multiscale method are optimized, and the multiscale characteristics of the convection-diffusion-reaction equations are demonstrated. The preliminary study on applications verifies the effectiveness of the present Fourier series multiscale method and provides a reliable reference which can be used for persistent improvement in computational performance of other multiscale methods.
翻译:在第四份论文中,将采用Fourier系列多尺度方法对一维和二维对流扩散反应方程式应用Fourier多尺度方法,得出Fourier系列多尺度解决办法,用数字实例调查Fourier系列多尺度解决办法的趋同特点,优化Fourier系列多尺度方法的应用办法,并演示对流-扩散-反应方程式的多尺度特性。关于应用的初步研究核实了目前四级对流-扩散反应方程式的有效性,提供了可靠的参考,可用于持续改进其他多尺度方法的计算性能。