In our project we discuss a finite element time-relaxation method for high Reynolds number flows. The key idea consists of using local projections on polynomials defined on macro element of each pair of two elements sharing a face. We give the formulation for the scalar convection–diffusion equation and a numerical illustration.

Indiana University-Purdue University Indianapolis (IUPUI) / In this thesis, an explicit time integration code which integrates multibody dynamics and the discrete element method is used for modelling the excavation and moving operation of cohesive soft soil (such as mud and snow) by bulldozers. A soft cohesive soil material model (that includes normal and tangential inter-particle force models) is used that can account for soil compressibility, plasticity, fracture, friction, viscosity and gain in cohesive strength due to compression. In addition, a time relaxation sub-model for the soil plastic deformation and cohesive strength is added in order to account for loss in soil cohesive strength and reduced bulk density due to tension or removal of the compression. This is essential in earth moving applications since the soil that is dug typically becomes loose soil that has lower shear strength and lower bulk density (larger volume) than compacted soil. If the model does not account for loss of soil shear strength then the dug soil pile in front of the blade of a bulldozer will have an artificially high shear strength. A penalty technique is used to impose joint and normal contact constraints. An asperity-based friction model is used to model contact and joint friction. A Cartesian Eulerian grid contact search algorithm is used to allow fast contact detection between particles. A recursive bounding box contact search algorithm is used to allow fast contact detection between the particles and polygonal contact surfaces. A multibody dynamics bulldozer model is created which includes the chassis/body, C-frame, blade, wheels and hydraulic actuators. The components are modelled as rigid bodies and are connected using revolute and prismatic joints. Rotary actuators along with PD (Proportional-Derivative) controllers are used to drive the wheels. Linear actuators along with PD controllers are used to drive the hydraulic actuators. Polygonal contact surfaces are defined for the tires and blade to model the interaction between the soil and the bulldozer. Simulations of a bulldozer performing typical shallow digging operations in a cohesive soil are presented. The simulation of a rear wheel drive bulldozer shows that, it has a limited digging capacity compared to the 4-wheel drive bulldozer. The effect of the relaxation parameter can be easily observed from the variation in the Bulldozer's velocity. The higher the relaxation parameter, the higher is the bulldozer's velocity while it is crossing over the soil patch. For the low penetration depth run the bulldozer takes less time compared to high penetration depth. Also higher magnitudes of torques at front and rear wheels can be observed in case of high penetration depth. The model is used to predict the wheel torque, wheel speed, vehicle speed and actuator forces during shallow digging operations on three types of soils and at two blade penetration depths. The model presented can be used to predict the motion, loads and required actuators forces and to improve the design of the various bulldozer components such as the blade, tires, engine and hydraulic actuators.