【摘要】 本文为Cahn-Hilliard-Navier-Stokes方程构造了一类新的高效并且高精度的数值格式.该格式基于两种类型的标量辅助变量，并且结合新的压力校正方法,大大提高了压力的精度.此外,该数值算法仅需在每个时间步长内求解一系列具有常系数的完全解耦的线性方程.最后,本文严格地证明了所提数值格式的无条件能量稳定性,并且通过数值模拟验证了算法的收敛阶,稳定性和有效性.更多还原

【Abstract】 In this paper, we construct a new class of efficient and high-order schemes for the Cahn-Hilliard-Navier-Stokes equations with periodic boundary conditions. These schemes are based on two types of scalar auxiliary variable approaches. By using a new pressure correction method, the accuracy of the pressure has been greatly improved.Furthermore, one only needs to solve a series of fully decoupled linear equations with constant coefficients at each time step. In addition, we prove the unconditional energy stability of the schemes, rigorously. Finally, plenty of numerical simulations are carried out to verify the convergence rates, stability, and effectiveness of the proposed schemes numerically.更多还原