Viscoelastic fluids are common in various industrial applications, including adhesive extrusion and application of sealant on automotive bodies, 3D-printing and polymer processing. Viscoelastic flows are however complex and time consuming to simulate numerically. In turn, real viscoelastic materials typically need to be modelled using multiple relaxation modes, which further increases the required CPU time. At the same time, calculation on graphical processing units (GPU) can provide significant speedup of numerical simulations.
In a recent publication we presented a Lagrangian-Eulerian method to simulate viscoelastic fluid flow. The constitutive equation is solved in Lagrangian nodes and the fluid momentum and continuity equations are solved on an Eulerian grid using the finite volume method. Interior objects are treated using the mirroring immersed boundary method. The coupling between the equations is established through robust interpolation using radial basis functions.
In this work, we show that the method can be extended to calculate the viscoelastic stresses using the GPU. A major advantage is that the Lagrangian method used to solve the constitutive equation is mesh-free and trivially parallelizable. The method is therefore very suitable for GPU-acceleration. The largest gain in simulation speed is typically found for larger problems, since the bandwidth of transferring data between the CPU and the GPU could be a limiting factor. The scaling of the computational performance with respect to the size of the problem is therefore studied, aswell as the computational cost for the different parts of the algorithm. For this, viscoelastic flows with both single and multiple relaxation modes are simulated. A significant increase of the overall simulation speed is found, as the time for calculating the stresses is heavily reduced.