非等温流动问题的无网格CBS方法模拟

Characteristic Based Split Meshfree Method for Non-isothermal Flow Problems

将特征线分步(Characteristic-based Split,CBS)法拓展到无网格方法中,提出了无网格CBS方法,并用其模拟了非等温流动问题.由于该方法采用了分步算法,所以能避开BB条件,使速度-压力采用等低阶基近似;另外由于在离散过程中采用了特征Galerkin(Characteristic Galerkin,CG)方法,其又能对对流占优问题起到很好的稳定作用,且不含任何依赖于网格的稳定化参数.最后,本文用其模拟了方腔自然对流问题,数值结果表明无网格CBS方法在求解非等温流动问题时能有效地消除对流占优引起的速度场、温度场振荡和速度与压力失耦现象,且具有很高的计算精度和较好的稳定性.

The characteristic based split （CBS）method was extended into the meshfree method, namely the meshfree CBS method was proposed for the non-isotheral incompressible flow problem. First, because this method was based on the split method, it avoided the BB condition and allowed the equal order basis for the velocity and the pressure. On the other hand, because this method was also discretized by the characteristic Galerkin（CG） method, it eliminated the spurious oscillations when the convection was dominated. Moreover, this method was not involved the choice of stability parameters which was dependent on mesh. Finally, the natural convection in a square cavity was simulated and the numerical results show that the meshfree CBS method can overcome spurious oscillations of velocity and temperature when the convection is dominated;meanwhile it can also eliminate numerical instability due to the improper coupling of velocity and pressure. Additionally, it is also observed that this method has fair stability and good accuracy .