Lagrangian Differencing Dynamics for Time-Independent Non-Newtonian Materials

This paper introduces a novel meshless and Lagrangian approach for simulating non-Newtonian flows, named Lagrangian Differencing Dynamics (LDD). Second-order-consistent spatial operators are used to directly discretize and solve generalized Navier–Stokes equations in a strong formulation. The solution is obtained using a split-step scheme, i.e., by decoupling the solutions of the pressure and velocity. The pressure is obtained by solving a Poisson equation, and the velocity is solved in a semi-implicit formulation. The matrix-free solution to the equations, and Lagrangian advection of mesh-free nodes allowed for a fully parallelized implementation on the CPU and GPU, which ensured an affordable computing time and large time steps. A set of four benchmarks are presented to demonstrate the robustness and accuracy of the proposed formulation. The tested two- and three-dimensional simulations used Power Law, Casson and Bingham models. An Abram slump test and a dam break test were performed using the Bingham model, yielding visual and numerical results in accordance with the experimental data. A square lid-driven cavity was tested using the Casson model, while the Power Law model was used for a skewed lid-driven cavity test. The simulation results of the lid-driven cavity tests are in good agreement with velocity profiles and stream lines of published reports. A fully implicit scheme will be introduced in future work. As the method precisely reproduces the pressure field, non-Newtonian models that strongly depend on the pressure will be validated.

Evaluation of Debris Flows for Flood Plain Estimation in a Small Ungauged Tropical Watershed for Hurricane Otto

The variability of climate, increase in population, and lack of territorial plans in Costa Rica have caused intense disasters with human and economic losses. In 2016, Hurricane Otto hit the country’s northern area, leaving substantial damages, including landslides, debris flows, and flooding. The present study evaluated different scenarios to estimate flooded areas for Newtonian (clean water), and non-Newtonian flows with volumetric sediment concentrations (Cv) of 0.3, 0.45, 0.55, and 0.65 using Hydro-Estimator (HE), rain gauge station, and the 100-year return period event. HEC–HMS modeled the rainfall products, and FLO-2D modeled the hydrographs and Cv combinations. The simulation results were evaluated with continuous statistics, contingency table, Nash Sutcliffe Efficiency, measure of fit (F), and mean absolute differences (E) in the floodplains. Flow depths, velocities, and hazard intensities were obtained in the floodplain. The debris flood was validated with field data and classified with a Cv of 0.45, presenting lower MAE and RMSE. Results indicated no significant differences in flood depths between hydrological scenarios with clean-water simulations with a difference of 8.38% in the peak flow. The flood plain generated with HE rainfall and clear-water condition presented similar results compared to the rain gauge input source. Additionally, hydraulic results with HE and Cv of 0.45 presented E and F values similar to the simulation of Cv of 0.3, demonstrating that the HE bias did not influence the determination of the floodplain depth and extent. A mean bias factor can be applied to a sub-daily temporal resolution to enhance HE rain rate quantifications and floodplain determination.

Powell-Eyring fluid flow over a stratified sheet through porous medium with thermal radiation and viscous dissipation

<abstract><p>The present study explores the effects of viscous dissipation, the thermal dependent conductivity and the thermal dependent viscosity on the steady motion of a Powell-Eyring fluid over a stratified stretching sheet which embedded in a porous medium. The fact that the nature of non-Newtonian flows problems are highly nonlinear equations has been taken into consideration here and this was the motive objective to determine numerical solutions. So, the emphasis is on the methodology adopted for obtaining numerical solutions that yielded after employing the Chebyshev spectral method. The temperature distributions and the velocity components are evaluated by solving numerically the boundary value problems that correspond to the proposed problem. Then, some figures have been plotted to elucidates the effect of different physical parameters appearing in the problem on both the temperature and the velocity profiles. The presence of the thermal radiation and the viscous dissipation in the fluid flow are shown to have quite a dramatic effect on the temperature profiles. In culmination, cooling process in nuclear reactors and geothermal engineering especially in the presence of thermal stratification phenomenon can be adopted as an application of this study. The theoretical and the observed results provide a fairly good qualitative agreement.</p></abstract>