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.

Ventricle-valve-aorta flow analysis with the Space–Time Isogeometric Discretization and Topology Change

“…The ST-SI introduced in [7] for the coupled incompressible-flow and thermal-transport equations retains the high-resolution representation of the thermo-fluid boundary layers near spinning solid surfaces. These ST-SI methods have been applied to aerodynamic analysis of vertical-axis wind turbines [6,46,47], thermo-fluid analysis of disk brakes [7], flow-driven string dynamics in turbomachinery [114][115][116], flow analysis of turbocharger turbines [11,[117][118][119][120], flow around tires with road contact and deformation [2,13,109,121,122], fluid films [13,123], aerodynamic analysis of ram-air parachutes [124], and flow analysis of heart valves [1,106,108,110,111].…”

“…By collapsing elements as needed, without changing the connectivity of the "parent" mesh, the ST-TC can handle an actual TC while maintaining high-resolution boundary layer representation near solid surfaces. This enabled successful moving-mesh computation of heart valve flows [1,8,9,95,106,[108][109][110][111], wing clapping [8,100], flow around a rotating tire with road contact and prescribed deformation [2,13,109,121,122], and fluid films [13,123].…”

“…It also enables dealing with contact location change and contact sliding. This was applied to heart valve flow analysis [1,106,108,110,111], tire aerodynamics with road contact and deformation [2,13,109,121,122], and fluid films [13,123].…”

A node-numbering-invariant directional length scale for simplex elements

“…119 for the coupled incompressible-flow and thermal-transport equations retains the high-resolution representation of the thermo-fluid boundary layers near spinning solid surfaces. These ST-SI methods have been applied to aerodynamic analysis of vertical-axis wind turbines, 98,48,49 thermo-fluid analysis of disk brakes, 119 flow-driven string dynamics in turbomachinery, [120][121][122] flow analysis of turbocharger turbines, [123][124][125][126] flow around tires with road contact and deformation, 115,[127][128][129][130] fluid films, 131,130 aerodynamic analysis of ram-air parachutes, 132 and flow analysis of heart valves. 116,117,111,113 In the ST-SI version presented in Ref.…”

“…It has been used in ST computational flow analysis of turbocharger turbines, [123][124][125][126] flow-driven string dynamics in turbomachinery, 121,122 ram-air parachutes, 132 spacecraft parachutes, 134 aortas, [111][112][113] heart valves, 116,117,111,113 tires with road contact and deformation, [128][129][130] and fluid films. 131,130 Using IGA basis functions in space is now a key part of some of the newest arterial zero-stress-state estimation methods [138][139][140][141]113 and related shell analysis. 142…”