论文标题
人工粘度对线性双曲系统的数值边界反馈控制的影响
The effect of artificial viscosity on numerical boundary feedback control of linear hyperbolic systems
论文作者
论文摘要
为了了解数值扩散对数值边界反馈控制的影响，对人工粘度的影响进行了数值分析。该分析是对使用上风方案离散的线性双曲线系统进行的。上风方案以最高二阶精度解决了对流扩散方程。分析表明，具有CFL等于一个的前风方案将预期的理论衰减达到一阶。另一方面，CFL少于CFL的上风方案会根据数据的第二个导数和CFL编号给出衰减。此外，如果溶液的第二个衍生物很小，则衰减速率会恶化。因此，与理论预测相比，数值方案计算出的衰减率往往更高。对测试用例的计算，包括等温欧拉和St Venant方程式证实了分析结果。
A numerical analysis of the effect of artificial viscosity is undertaken in order to understand the effect of numerical diffusion on numerical boundary feedback control. The analysis is undertaken on the linear hyperbolic systems discretised using the upwind scheme. The upwind scheme solves the advection-diffusion equation with up to second-order accuracy. The analysis shows that the upwind scheme with CFL equal to one gives the expected theoretical decay up to first-order. On the other hand the upwind scheme with CFL less than one gives decay depending on the second derivative of the data and the CFL number. Further the decay rates deteriorate if the second derivatives of the solution are small. Thus the decay rates computed by the numerical schemes tend to be higher in comparison to the theoretical prediction. Computations on test cases which include isothermal Euler and the St Venant Equations confirm the analytical results.
