Analysis of the Shear-Thinning Viscosity Behavior of the Johnson–Segalman Viscoelastic Fluids

This paper presents a numerical comparison of viscoelastic shear-thinning fluid flow using a generalized Oldroyd-B model and Johnson–Segalman model under various settings. Results for the standard shear-thinning generalization of Oldroyd-B model are used as a reference for comparison with those obtained for the same flow cases using Johnson–Segalman model that has specific adjustment of convected derivative to assure shear-thinning behavior. The modeling strategy is first briefly described, pointing out the main differences between the generalized Oldroyd-B model (using the Cross model for shear-thinning viscosity) and the Johnson–Segalman model operating in shear-thinning regime. Then, both models are used for blood flow simulation in an idealized stenosed axisymmetric vessel under different flow rates for various model parameters. The simulations are performed using an in-house numerical code based on finite-volume discretization. The obtained results are mutually compared and discussed in detail, focusing on the qualitative assessment of the most distinct flow field differences. It is shown that despite all models sharing the same asymptotic viscosities, the behavior of the Johnson–Segalman model can be (depending on flow regime) quite different from the predictions of the generalized Oldroyd-B model.

Consistency and convergence for a family of finite volume discretizations of the Fokker–Planck operator

We introduce a family of various finite volume discretization schemes for the Fokker–Planck operator, which are characterized by different Stolarsky weight functions on the edges. This family particularly includes the well-established Scharfetter–Gummel discretization as well as the recently developed square-root approximation (SQRA) scheme. We motivate this family of discretizations both from the numerical and the modeling point of view and provide a uniform consistency and error analysis. Our main results state that the convergence order primarily depends on the quality of the mesh and in second place on the choice of the Stolarsky weights. We show that the Scharfetter–Gummel scheme has the analytically best convergence properties but also that there exists a whole branch of Stolarsky means with the same convergence quality. We show by numerical experiments that for small convection the choice of the optimal representative of the discretization family is highly non-trivial while for large gradients the Scharfetter–Gummel scheme stands out compared to the others.

A three-dimensional model of transient bioheat transfer in the lower extremity during cryotherapy

The purpose of this research was to create a computational model of the human thigh undergoing cryotherapy. The tissue temperatures were measured for five cold pack temperatures of −8°C, −4°C, 0°C, 4°C, and 8°C in addition to six different time intervals of cold application and ice removal. The depth of cold penetration and duration of local tissue cooling were investigated at 10 points during 30 min of application and 7 h of post-application. The model was created in CATIA, using a mid-axial cut of the human thigh MRI without pathology. After validation by the available clinical data, this research applied the finite-volume discretization method to solve bioheat transfer equations. A 16°C decrease in the cold pack temperature reduced the tissue temperatures located 1 and 2 cm below the fat by almost 3.34°C and 1.4°C, respectively, after 30 min of cold application. It took the tissues 10–15 min to start cooling down, and the temperature reached its plateau after 100 min. Thirty minutes of cold application declined the superficial tissue and deep tissue temperatures near the bone by 22.59°C and 0.48°C, respectively. Intense cryotherapy led to an insignificant change in the deep tissue temperature at 2 cm and deeper below the fat tissue. After ice removal, tissues continued cooling down for about 8 min until 40 min, depending on the tissue depth. This study proposed a 100-min cold therapy with 10 min of ice removal to optimize tissue cooling.

A Consistent and Implicit Rhie–Chow Interpolation for Drag Forces in Coupled Multiphase Solvers

The use of coupled algorithms for single fluid flow simulation has proven its superiority as opposed to segregated algorithms, especially in terms of robustness and performance. In this paper, the coupled approach is extended for the simulation of multi-fluid flows, using a collocated and pressure-based finite volume discretization technique with a Eulerian–Eulerian model. In this context a key ingredient in this method is extending the Rhie–Chow interpolation technique to account for the unique flow coupling that arises from inter-phase drag. The treatment of this inter-fluid coupling and the fashion in which it interacts with the velocity-pressure solution algorithm is presented in detail and its effect on robustness and accuracy is demonstrated using 2D dilute gas–solid flow test case. The results achieved with this technique show substantial improvement in accuracy and performance when compared to a leading commercial code for a transonic nozzle configuration.

Extending the global-direction stencil with “face-area-weighted centroid” to unstructured finite volume discretization from integral form

Accuracy of unstructured finite volume discretization is greatly influenced by the gradient reconstruction. For the commonly used k-exact reconstruction method, the cell centroid is always chosen as the reference point to formulate the reconstructed function. But in some practical problems, such as the boundary layer, cells in this area are always set with high aspect ratio to improve the local field resolution, and if geometric centroid is still utilized for the spatial discretization, the severe grid skewness cannot be avoided, which is adverse to the numerical performance of unstructured finite volume solver. In previous work [Kong, et al. Chin Phys B 29(10):100203, 2020], we explored a novel global-direction stencil and combined it with the face-area-weighted centroid on unstructured finite volume methods from differential form to realize the skewness reduction and a better reflection of flow anisotropy. Greatly inspired by the differential form, in this research, we demonstrate that it is also feasible to extend this novel method to the unstructured finite volume discretization from integral form on both second and third-order finite volume solver. Numerical examples governed by linear convective, Euler and Laplacian equations are utilized to examine the correctness as well as effectiveness of this extension. Compared with traditional vertex-neighbor and face-neighbor stencils based on the geometric centroid, the grid skewness is almost eliminated and computational accuracy as well as convergence rate is greatly improved by the global-direction stencil with face-area-weighted centroid. As a result, on unstructured finite volume discretization from integral form, the method also has superiorities on both computational accuracy and convergence rate.