Curvilinear Finite Difference Method Research Articles

A Study on the role of hydraulic retention time in eutrophication of the asahi river dam reservoir

The Asahi River Dam reservoir is one of the important freshwater resources for Okayama City, Japan. The eutrophication of the reservoir has been warned of since the 1980s. In this study, we discuss the relationship between hydraulic retention time and increase of phytoplankton, and the influence of wind-driven currents on the spatial distribution of phytoplankton based on the observations and numerical simulations. Observations were carried out from 1993 to 1995. The numerical simulation of hydraulics in the reservoir was carried out by applying an orthogonal curvilinear finite difference method. Judging from phosphorus and nitrogen concentrations, the water quality of the Asahi River Dam reservoir is usually eutrophic. However, high concentrations of chlorophyll-a are not always observed. The observed dependence of chlorophyll-a concentration on hydraulic retention time is reproduced fairly well by a simple relationship derived from the balance of phytoplankton based on the assumption of complete mixing. The hydraulic retention time is a limiting factor of an increase in phytoplankton in the Asahi River Dam reservoir. It takes a retention time of 2 weeks for the sufficient increase of phytoplankton. The results obtained by the simulations show that the wind-driven currents play an important role in the spatial distribution of phytoplankton.

An improved curvilinear finite difference (CFD) method for arbitrary mesh systems

This paper describes the automatic computer generation of finite difference approximations for partial derivatives in arbitrary mesh systems using an “Improved CFD” method. In the first part of the paper, the algorithm of the proposed Improved CFD method, used to solve a general second-order linear partial differential equation defined in a two-dimensional domain, will be presented. The performance of this numerical method will then be compared with the “Original CFD” method developed by Lau[1], and a so-called least square surface fit method developed by Liszka and Orkisz[2]. In the proposed method, extensive use is made of matrix algebra. The method is therefore highly systematic and can be easily implemented into computer programmes. Numerical examples tested in this paper indicate that, for irregular meshes, better numerical accuracy can be attained by the proposed method as compared with the Original CFD method. At the same time, the straightforward extension of the present method to the generation of higher-order-than-two finite difference approximations and to the solution of three-dimensional field problems will also be demonstrated. In the second part of the paper, the computational procedures for the numerical solution of a first boundaryvalue problem which is governed by a single second-order nonlinear partial differential equation will be derived.