An SPH Projection Method
An SPH Projection Method
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DOI：
10.1006/jcph.1999.6246
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发表时间：
1999-07
影响因子：
4.1
通讯作者：
S. J. Cummins;M. Rudman
中科院分区：
文献类型：
--
作者：
S. J. Cummins;M. Rudman
介绍了光滑粒子流体动力学（SPH）中一种新的不可压缩性公式。该方法使用分数阶，速度场在时间上向前积分，而不强制不可压缩。由此产生的中间速度场，然后投影到一个发散的自由空间，通过求解压力泊松方程从一个近似的压力投影。与早期使用SPH模拟不可压缩流的方法不同，压力不是热力学变量，柯朗条件仅基于流体速度而不是声速。虽然可以使用更大的时间步长，所得到的椭圆形压力泊松方程的解增加了每个时间步长的总功。效率比较表明，投影方法具有显着的潜力，以减少整体计算费用相比，弱可压缩SPH，特别是雷诺数，Re，增加。模拟使用SPH投影技术显示出良好的协议与有限差分解决方案的旋涡自旋下降和瑞利？泰勒不稳定性然而，结果表明，使用一个近似的投影，以加强不可压缩性导致误差积累的密度场。
A new formulation is introduced for enforcing incompressibility in Smoothed Particle Hydrodynamics (SPH). The method uses a fractional step with the velocity field integrated forward in time without enforcing incompressibility. The resulting intermediate velocity field is then projected onto a divergence-free space by solving a pressure Poisson equation derived from an approximate pressure projection. Unlike earlier approaches used to simulate incompressible flows with SPH, the pressure is not a thermodynamic variable and the Courant condition is based only on fluid velocities and not on the speed of sound. Although larger time-steps can be used, the solution of the resulting elliptic pressure Poisson equation increases the total work per time-step. Efficiency comparisons show that the projection method has a significant potential to reduce the overall computational expense compared to weakly compressible SPH, particularly as the Reynolds number, Re, is increased. Simulations using this SPH projection technique show good agreement with finite-difference solutions for a vortex spin-down and Rayleigh?Taylor instability. The results, however, indicate that the use of an approximate projection to enforce incompressibility leads to error accumulation in the density field.