The highly nonlinear nature of the system governing equations makes it difficult to simulate viscoelastic flows efficiently. In this paper, an implicit decoupling approach is proposed for the viscoelastic flow simulation with a monolithic projection method. The decoupling approach can be derived from the approximate block factorization at the matrix level, which has been successfully applied into the Newtonian flow simulations. In our work, we extend this approach to decouple the pressure, conformation tensor and velocity from the viscoelastic flow system sequentially. Firstly, the pressure-conformation tensor-velocity decoupling is realized by a two-step approximate factorization. By combining the conformation tensor and velocity together at the first-step factorization, the original efficient pressure Poisson solver for the Newtonian flow simulation can be directly adopted in the present framework for non-Newtonian flow simulation. Secondly, the conformation tensor components are further decoupled from each other by the present component-decoupling approach. Then all quantities, including pressure, conformation tensor and velocity, can be resolved without iteration. Additionally, the accuracy corrector is proposed to access the prior scheme limiter-estimation problem introduced by the implicit high-resolution scheme. We numerically demonstrate that all quantities preserve the second-order accuracy in time and space as expected by the theoretical splitting errors. Finally, several different types of canonical benchmark flow examples are conducted to validate the present solver, including laminar flow, turbulent drag-reducing flow and the rotation of a spherical particle immersed in a sheared viscoelastic fluid.

系统控制方程的高度非线性特性使得难以有效地模拟粘弹性流动。在本文中，提出了一种隐式解耦方法，用于使用整体投影方法进行粘弹性流动模拟。解耦方法可以从矩阵级别的近似块分解中推导出来，该方法已成功应用于牛顿流动模拟。在我们的工作中，我们扩展了这种方法，将压力、构象张量和速度从粘弹性流动系统中依次解耦。首先，通过两步近似分解来实现压力-构象张量-速度解耦。通过在第一步分解中将构象张量和速度组合在一起，牛顿流动模拟的原始高效压力泊松求解器可以直接用于当前的非牛顿流动模拟框架。其次，构象张量分量通过当前的分量解耦方法进一步相互解耦。然后所有量，包括压力、构象张量和速度，都可以在没有迭代的情况下求解。此外，提出了精度校正器来解决由隐式高分辨率方案引入的先验方案限制器估计问题。我们在数值上证明了所有量都保持了理论分裂误差所预期的时间和空间上的二阶精度。最后，进行了几种不同类型的规范基准流示例来验证当前的求解器，包括层流，