Dissipation pressure quotient (DPQ): A refined approach for meshing of cerebral venous geometries for high-fidelity computational fluid dynamics

Abstract

Recently we used high-fidelity computational fluid dynamics (CFD) simulations to demonstrate the relevance of high-frequency ($\sim 100-1000\mathrm{Hz}$) flow instabilities to clinical phenomena associated with cerebral venous disorders, such as pulsatile tinnitus (PT). We have previously demonstrated the challenges of a priori meshing of the tortuous venous sinus geometries and hence accurately computing the complex flow phenomena they engender, but also the invariance of bulk pressure phenomena with CFD resolution. Building on that work, here we propose a convergence criterion based on the viscous dissipation term from the work-energy relative pressure drop (WERP) form of the Navier–Stokes equations normalized by the total pressure drop – a quantity we term the dissipation-pressure quotient (DPQ). In the present study, DPQ was used to show, for three patient-specific geometries, that although qualitative differences in bulk flow patterns from a series of conventionally refined meshes were minimal, quantitatively the differences were not asymptotically converged. Nevertheless, the relative distribution of maximum viscous dissipation rate was comparable with mesh resolution, suggesting its use for identifying regions in the mesh requiring greater resolution a posteriori, even on under-resolved meshes, and marking them for refinement. Using DPQ as a convergence criterion, we show that this refinement strategy allows for more effective use of elements when executed from both moderate- and coarse-resolution starting meshes. Unlike conventional adaptive meshing, this strategy allows for multiple refinements to be run in parallel, permitting efficient verification studies within time frames necessary for clinical decision-making, and helps to overcome some of the guesswork involved with meshing of these complicated geometries, toward robust prediction of blood flow disturbances in cerebral venous disorders.