International Journal of Computational Engineering Science

A solution method based on a novel combination of the differential quadrature (DQ) method and the moving-least-squares (MLS) approximation is developed for solving the partial differential equations. The unknown variables in the domain are expressed in terms of the moving-least-squares approximation. The weight functions used in the differential quadrature method are calculated through a fast computation of the shape functions and their derivatives. The proposed method, called the moving least squares differential quadrature (MLSDQ) method, is applied to two-dimensional problems described by the Laplace and Poisson equations. Numerical experiments on MLSDQ method are presented for several example problems by considering the numerical accuracy, and h and p convergence. Sensitivity of the solution to the nodal patterns and effect of domains of influence are also carefully investigated.

Several explicit high resolution TVD methods and their detailed application to steady and unsteady one-dimensional free surface channel flow problems are presented. Some of these methods are widely presented in the literature. Their evaluation is based on computations performed for steady state benchmark problems with analytical solutions and for a wide range of cases, which include friction, nonuniform bed slopes, hydraulic jumps and non-prismatic channel cross sections. Results for the classical benchmark problem of an idealised dam-break are also presented. The results obtained by the various TVD methods are compared with each other and the exact solutions, providing insight into the limitations of the methods along with their relative performances in robustness and accuracy. Some subtle points of the methods and the effects of selecting different options for certain methods are emphasized.

A depth-integrated two-dimensional hydrodynamic and sediment transport model, CCHE2D, has been developed for analyzing free surface flows for general applications to hydraulic engineering problems. Mixed schemes of finite element method (Efficient Element Method) and finite volume method are adopted for solving momentum and continuity equations. A unique velocity correction method was developed to couple the governing equations. Pressure (free surface) field is discretized on a staggered grid. Two zero equation turbulence closure schemes: a depth averaged parabolic, a depth averaged mixing length eddy viscosity model, and a two-equation k-ε model for depth-averaged flows are included for different application needs. Algebraic systems of equations are solved implicitly by using SIP method. This model can be used for simulating steady and unsteady near field and natural river flows with relatively shallow water depth. Validation tests for this model show good agreements between the model prediction and data of physical models and field measurements.

We simulate scalar mixing and chemical reactions using the lattice Boltzmann method. Simulations of initially non-premixed binary mixtures yield scalar probability distribution functions that are in good agreement with direct numerical simulation (of Navier-Stokes equation) data. One-dimensional chemically-reacting flow simulation of a premixed mixture yields a flame speed that is consistent with experimentally determined value. These results serve to establish the feasibility of the lattice Boltzman method as a viable tool for computing turbulent combustion.

Inelastic stresses and displacements in rotating solid disks of exponentially varying thickness have been investigated using Tresca's and von Mises' yield criteria. In both criteria, linear strain hardening material behavior is assumed. A previously obtained analytical solution is adopted in the analysis when Tresca criterion is used. An efficient numerical solution procedure has been designed to obtain the solution of von Mises. Plastic limit angular velocities have been calculated for different values of the geometric parameters. In all the cases investigated the difference between Tresca and von Mises, in finding plastic limit angular velocities was less than 3%. The inelastic stresses, displacement and strains have been calculated for disks of different profiles and the results presented in graphical forms.