Burgers方程的跳点紧致格式

Burgers方程是流体力学中非常重要方程.通过Hopf-Cole变换可以将Burgers方程转化为抛物型方程,把为Burgers方程构造一种高精度的、高效率的数值格式的问题变成了为抛物型方程构造一种新格式的问题.新格式以等价于Du Fort-Frankel格式的跳点格式为基础,引入高阶紧致格式的思路以提高跳点格式的收敛阶,称新格式为跳点紧致格式.此格式既保持了跳点格式计算效率高、占用内存少、无条件稳定的优点,又将空间方向收敛阶由2阶提高到了4阶.最后,数值算例验证了跳点紧致格式在空间方向收敛阶是4阶的.

The Jumping and Compact Method for Burgers Equation

The Burgers equation is a very important model in fluid mechanics.It can be transformed into a general parabolic equation by a Hopf-Cole transformation.Then the problem about constructing a high accuracy and efficient method for Burgers equation has become a new problem for the parabolic equation.The new scheme is based on the jumping method which is equivalent to Du Fort-Frankel method.The high order compact methods are used to accelerate the convergent rate and it is called jumping and compact method.It maintains the advantages of highly computational efficiency,little memory and unconditional stability.Moreover,it also increases the convergent order in space from second to fourth.Lastly,a simple numerical example is introduced to verify that the convergent rate of the jumping and compact method in the space is of fourth order.