Space–time Isogeometric flow analysis with built-in Reynolds-equation limit

Abstract

We present a space–time (ST) computational flow analysis method with built-in Reynolds-equation limit. The method enables solution of lubrication fluid dynamics problems with a computational cost comparable to that of the Reynolds-equation model for the comparable solution quality, but with the computational flexibility to go beyond the limitations of the Reynolds-equation model. The key components of the method are the ST Variational Multiscale (ST-VMS) method, ST Isogeometric Analysis (ST-IGA), and the ST Slip Interface (ST-SI) method. The VMS feature of the ST-VMS serves as a numerical stabilization method with a good track record, the moving-mesh feature of the ST framework enables high-resolution flow computation near the moving fluid–solid interfaces, and the higher-order accuracy of the ST framework strengthens both features. The ST-IGA enables more accurate representation of the solid-surface geometries and increased accuracy in the flow solution in general. With the ST-IGA, even with just one quadratic NURBS element across the gap of the lubrication fluid dynamics problem, we reach a solution quality comparable to that of the Reynolds-equation model. The ST-SI enables moving-mesh computation when the spinning solid surface is noncircular. The mesh covering the solid surface spins with it, retaining the high-resolution representation of the flow near the surface, and the SI between the spinning mesh and the rest of the mesh accurately connects the two sides of the solution. We present detailed 2D test computations to show how the method performs compared to the Reynolds-equation model, compared to finite element discretization, at different circumferential and normal mesh refinement levels, when there is an SI in the mesh, and when the no-slip boundary conditions are weakly-enforced.