A recently proposed Lagrangian-Eulerian method for viscoelastic flow simulation is extended to high performance calculations on the Graphics Processing Unit (GPU). The two most computationally intensive parts of the algorithm are implemented for GPU calculation, namely the integration of the viscoelastic constitutive equation at the Lagrangian nodes and the interpolation of the resulting stresses to the cell centers of the Eulerian grid.

In the original CPU method, the constitutive equations are integrated with a second order backward differentiation formula, while with the proposed GPU method the implicit Euler method is used. To allow fair comparison, the latter is also implemented for the CPU. The methods are validated for two flows, a planar Poiseuille flow of an upper-convected Maxwell fluid and flow past a confined cylinder of a four-mode Phan Thien Tanner fluid, with identical results.

The calculation times for the methods are compared for a range of grid resolutions and numbers of CPU threads, revealing a significant reduction of the calculation time for the proposed GPU method. As an example, the total simulation time is roughly halved compared to the original CPU method. The integration of the constitutive equation itself is reduced by a factor 50 to 250 and the unstructured stress interpolation by a factor 15 to 60, depending on the number of CPU threads used.

最近提出的用于粘弹性流动模拟的拉格朗日-欧拉方法扩展到图形处理单元（GPU）上的高性能计算。该算法的两个计算量最大的部分用于GPU计算，即在Lagrangian节点上的粘弹性本构方程的积分和对欧拉网格的单元中心的所得应力的插值。

在原始的CPU方法中，本构方程与二阶后向微分公式集成在一起，而在建议的GPU方法中，使用隐式Euler方法。为了进行公平的比较，还为CPU实现了后者。该方法针对两种流动进行了验证：上部对流的麦克斯韦流体的平面Poiseuille流体和通过四模式Phan Thien Tanner流体的密闭圆柱体的流体，其结果相同。

针对各种网格分辨率和CPU线程数比较了这些方法的计算时间，从而显着减少了所建议的GPU方法的计算时间。例如，与原始CPU方法相比，总仿真时间大约减少了一半。根据所使用的CPU线程数，本构方程本身的积分减少50到250倍，非结构化应力插值减少15到60倍。