完全变光滑长度SPH法及其实现

提出完全变光滑长度SPH法及其算法实现.方程组基于对称形式核函数近似,SPH密度演化方程与变光滑长度方程隐式关联;在Springel提出的全守恒SPH方程组基础上,通过将分散核近似形式改进为对称核近似形式得到SPH动量方程和能量方程.采用迭代求解密度演化方程和变光滑长度方程,显式求解SPH动量方程和能量方程,增加的计算量相对很少.给出三个1D激波管算例和2D Sedov算例验证方法的有效性.数值结果表明,算法保持动量和能量的守恒律,解决了传统SPH法中由于变光滑长度影响带来的计算误差,且在模拟2DSedov问题时能得到比Springel方法更准确的压强峰值位置和中心压强值.特别适合于模拟爆炸与冲击、大变形大扭曲等密度梯度和光滑长度梯度剧烈变化的问题.

SPH Method with Fully Variable Smoothing Lengths and Implementation

SPH(smoothed particle hydrodnamics) method with fully variable smoothing lengths is proposed.Different from existing adaptive kernel SPH methods,fully variable smoothing lengths are considered based on an adaptive symmetrical kernel estimation.An evolution equation of density is derived which implicitly couples with a variable smoothing length equation.Based on Springel's fully conservative formulation SPH momentum equation and energy equation are derived by using symmetrical kernel estimation instead of scatter kernel estimation.An additional iteration process is employed to solve evolution equations of density and variable smoothing lengths equation.SPH momentum equation and energy equation are solved explicitly.Computation cost added by iteration is little.The equations and algorithm are tested via three 1D shock-tube problems and a 2D Sedov problem.It is showed that conservation of momentum and energy is improved substantially and variable smoothing lengths effect is corrected,especially in the 2D Sedov problem.Pressure peak position and pressure at center are more accurate than those by Springel's scheme.The method deals with large density gradient and large smoothing length gradient problems well,such as large deformation and serious distortion problems in high velocity impact and blasting.