Meshless analysis of flow and concentration in a water reservoir

Abstract

In an earlier study, a boundary element methodology was developed to obtain numerically stable and convergent results for the concentration distribution and flow of a water reservoir. In the process to apply the boundary element method to the flow analysis around a machine that supplies dissolved oxygen (DO), we realised that the divergence and accuracy of the very delicate flow were sensitive to the mesh (domain) and boundary discretisation. In other words, it seemed difficult to determine the appropriate lengths of the mesh (domain) and boundary discretisation for obtaining stability and convergence in the computational analysis. In this paper, a new meshless method is presented, which overcomes the difficulties of the boundary element method described above. The method is based on the idea of mesh-free radial basis functions (RBFs), which is a collocation method. Referring to the velocity vectors of the water flow calculated by the weighted finite difference method (WFDM) and the finite element method (FEM) and observed in the model simulation of a water reservoir constructed in the sanitary and environmental engineering laboratory of Kyushu Sangyo University, the effect and accuracy of the alternative meshless method were estimated. Keywords: flow and concentration in water reservoirs, meshless method, weighted finite difference method, finite element method, observed velocity in model simulation of water reservoir.

Meshless and BE analysis of the flow and concentration around a DO-supplying machine

“…where λ means R e ・ K/ρ, R e is the Reynolds number, and K describes the coefficient of the penalty method (Kanoh et al [1,2]). …”

“…First of all, the concentration in the steady state is expressed as Equation (9) with Equation (10) (Kanoh et al [1]). …”

“…The meshless method is based on the idea of the mesh-free RBF collocation method (Kanoh et al [1]). The penalty method was used so that the pressure terms would be eliminated in the N-S equations and the difficulty of the pressure boundary conditions would be avoided in the meshless method.…”

“…The boundary conditions for the flow and concentration analyses have been previously proposed for the meshless method, the BEM, the FEM, and the WFDM (Kanoh et al [1][2][3]). Regarding the boundary discretisation for the flow analysis by our boundary element method, the outline is as follows: (1) the convergence and accuracy of the very delicate flow were sensitive to the domain and boundary discretisation.…”

“…By using a machine that supplies DO (dissolved oxygen), we attempted to ameliorate the concentration of oxygen in the lower layer of water areas, such as a water reservoir or the sea (Kanoh et al [1]), and succeeded in several cases. Our DO-supplying machine dissolved the high concentration of oxygen (about 100 mg per litre: [mg/L]) in the water of the tank of the machine at a depth of about 50 metres.…”