数值弥散 meaning in Chinese
numerical dispersion
Examples
- The characteristic approximation is used to handle the convection part along the direc - tion of fluid namely characteristic direction to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion ; the mixed finite element spatial approximation is employed to deal with diffusion part and approximate the scalar unknown and the adjoint vector function optimally and simultaneously ; in order to preserve the integral conservation of the method , we introduce the modified characteristic method
该方法对方程的对流部分沿流体流动的方向即特征方向离散以保证格式在流动的锋线前沿逼近的高稳定性，消除数值弥散现象；对方程的扩散部分采用最低次混合有限元方法离散、同时以高精度逼近未知函数及未知函数的梯度；为保证方法的整体守恒性，在格式中引入修正项 - In chapter one , we propose a new mixed method called characteristics mixed finite element method for a convection - dominated diffusion problems with small parameter e : we handle the convection part whth backward difference scheme along the characteristics , obtain much smaller time - trunction errors and avoid numerical dispersion on the front of the peak curve of the flow : we use a lowest order mixed finite element method to deal with the diffusion part , so this scheme can approximate the unknow function and its following vector with high accuracy at the same time
第一章中我们对小参数对流占优扩散问题提出了新的数值方法? ?特征混合有限元方法，即对方程的对流部分采用沿特征线的后退差分格式求解，以保证较小的截断误差限并避免了在流动的锋线前沿数值弥散现象的出现；对流动的扩散部分采用最低次混合元方法求解，以保证格式对未知函数及伴随向量的同时高精度逼近。由于该方法中检验函数可取分片常数，此格式在某种意义上具有局部守恒性质。 - The new method is a combination of characteristic approximation to handle the convection part , to ensure the high stability of the method in approximating the sharp fronts and reduce the numerical diffusion , a smaller time truncation is gained at the same time , and a mixed finite element spatial approximation to deal with the diffusion part , the sealer unknown and the adjoint vector function are approximated optimally and simultaneously
此方法即为对方程的对流项沿流体流动的方向即特征方向进行离散，从而保证格式在流动锋线前沿逼近的高稳定性，消除了数值弥散现象，并得到了较小的时间截断误差；另一方面，对方程的扩散项采用混合元离散，可同时高精度逼近未知函数及其伴随向量函数，理论分析表明，此方法是稳定的，具有最优的l ~ 2逼近精度。