A new type of boundary integral-equation for plane problems of elasticity including rotational forces

Based on the idea proposed by Hu [Scientia Sinica Series A XXX, 385-390 (1987)], a new type of boundary integral equation for plane problems of elasticity including rotational forces is derived and its boundary element formulation is presented. Numerical results for a rotating hollow disk are given to demonstrate the accuracy of the new type of boundary integral equation.

Evaluation of macrophyte control in 38 Florida lakes using triploid grass carp

Florida’s large number of shallow lakes, warm climate and long growing season have contributed to the development of excessive growths of aquatic macrophytes that have seriously interfered with many water use activities. The introduction of exotic aquatic macrophyte species such as hydrilla ( Hydrilla verticillata ) have added significantly to aquatic plant problems in Florida lakes. The use of grass carp ( Ctenopharyngodon idella ) can be an effective and economical control for aquatic vegetation such as hydrilla. Early stocking rates (24 to 74 grass carp per hectare of lake area) resulted in grass carp consumption rates that vastly exceeded the growth rates of the aquatic plants and often resulted in the total loss of all submersed vegetation. This study looked at 38 Florida lakes that had been stocked with grass carp for 3 to 10 years with stocking rates ranging from < 1 to 59 grass carp per hectare of lake and 1 to 207 grass carp per hectare of vegetation to determine the long term effects of grass carp on aquatic macrophyte communities. The median PAC (percent area coverage) value of aquatic macrophytes for the study lakes after they were stocked with grass carp was 14% and the median PVI (percent volume infested) value of aquatic macrophytes was 2%. Only lakes stocked with less than 25 to 30 fish per hectare of vegetation tended to have higher than median PAC and PVI values. When grass carp are stocked at levels of > 25 to 30 fish per hectare of vegetation the complete control of aquatic vegetation can be achieved, with the exception of a few species of plants that grass carp have extreme difficulty consuming. If the management goal for a lake is to control some of the problem aquatic plants while maintaining a small population of predominately unpalatable aquatic plants, grass carp can be stocked at approximately 25 to 30 fish per hectare of vegetation.

Numerical-Value Perturbation Method with Application of Solving Convective-Diffusion Integral Equation

The convective--diffusion equation is of primary importance in such fields as fluid dynamics and heat transfer hi the numerical methods solving the convective-diffusion equation, the finite volume method can use conveniently diversified grids (structured and unstructured grids) and is suitable for very complex geometry The disadvantage of FV methods compared to the finite difference method is that FV-methods of order higher than second are more difficult to develop in three-dimensional cases. The second-order central scheme (2cs) offers a good compromise among accuracy, simplicity and efficiency, however, it will produce oscillatory solutions when the grid Reynolds numbers are large and then very fine grids are required to obtain accurate solution. The simplest first-order upwind (IUW) scheme satisfies the convective boundedness criteria, however. Its numerical diffusion is large. The power-law scheme, QMCK and second-order upwind (2UW) schemes are also often used in some commercial codes. Their numerical accurate are roughly consistent with that of ZCS. Therefore, it is meaningful to offer higher-accurate three point FV scheme. In this paper, the numerical-value perturbational method suggested by Zhi Gao is used to develop an upwind and mixed FV scheme using any higher-order interpolation and second-order integration approximations, which is called perturbational finite volume (PFV) scheme. The PFV scheme uses the least nodes similar to the standard three-point schemes, namely, the number of the nodes needed equals to unity plus the face-number of the control volume. For instanc6, in the two-dimensional (2-D) case, only four nodes for the triangle grids and five nodes for the Cartesian grids are utilized, respectively. The PFV scheme is applied on a number of 1-D problems, 2~Dand 3-D flow model equations. Comparing with other standard three-point schemes, The PFV scheme has much smaller numerical diffusion than the first-order upwind (IUW) scheme, its numerical accuracy are also higher than the second-order central scheme (2CS), the power-law scheme (PLS), the QUICK scheme and the second-order upwind(ZUW) scheme.