A weakly compressible moving particle semi-implicit (WC-MPS) method is utilized to simulate non-Newtonian free surface flows due to the advantages of particle methods with respect to handling large deformation and fragmentation. The Cross rheology equation was selected in order to capture the viscous features of the mixture flows. To numerically implement the Cross equation, an experiment-based method was proposed to determine the four rheology parameters in the equation. The method of using a WC-MPS model to study non-Newtonian dam break flow problems was then adopted. The capabilities of the proposed method were tested by simulating different materials with the proposed method in modeling non-Newtonian free surface flows. Significant viscous features were reproduced by the proposed model.

Dealing with large deformation and fragmentation of geometries and interfaces (e.g., free surfaces), the regular mesh-based Eulerian methods, such as finite-element and finite-difference methods, have difficulties in fluid-flow modeling. Recently, studies have focused on a new generation of numerical methods called mesh-free particle (Lagrangian) methods. In this study, a mesh-free particle method based on the moving-particle semi-implicit (MPS) particle-interaction model has been developed for simulation of open-channel flow. The model is able to simulate viscous fluid flow with large deformation and fragmentation of free surface in practical fields. Moreover, the model is capable of modeling open-channel problems with both inflow and outflow and inconstant numbers of particles. The model has been validated and applied to some common sample problems. The results show the reasonable accuracy of the model. The final model is capable of modeling free-surface deformation and fragmentation as well as accurate...

Semianalytical equations were derived for distribution of shear stress in straight open channels with rectangular, trapezoidal, and compound cross sections. These equations are based on a simplified streamwise vorticity equation that includes secondary Reynolds stresses. Reynolds stresses were then modeled and their different terms were evaluated based on the work of previous researchers and experimental data. Substitution of these terms into the simplified vorticity equation yielded the relative shear stress distribution equation along the width of different channel cross sections. In compound channels the effect of additional secondary flows due to the shear layer between the main channel and the flood plain were also considered. Comparisons between predictions of the model and experimental data, predictions of other analytical or three dimensional numerical models with advanced turbulent closures, were made with good agreement.

A two-dimensional depth averaged model is developed in a nonorthogonal curvilinear coordinate system. The ability of the model in handling complex mesh arrangements with high aspect ratios and skewness is investigated. It is shown that model formulation makes it able to handle large skewness in the grid lines. It is also shown that in predicting the water surface profile with a very distorted mesh, most of the errors arise from the large aspect ratio rather than the skewness of the grid lines. The model is then applied to three meandering channels (two simple and one compound), with specifications similar to those found in nature and the results are compared with experimental data. The comparison shows that the model predicted the water surface profile and velocity distribution well in simple channels. Predictions of the model in the main channel of the compound meandering channel were also in general agreement with the experimental results.