A Numerical Treatment of Nondimensional Form of Water Quality Model in a Nonuniform Flow Stream Using Saulyev Scheme

Abstract

The stream water quality model of water quality assessment problems often involves numerical methods to solve the equations. The governing equation of the uniform flow model is one-dimensional advection-dispersion-reaction equations (ADREs). In this paper, a better finite difference scheme for solving ADRE is focused, and the effect of nonuniform water flows in a stream is considered. Two mathematical models are used to simulate pollution due to sewage effluent. The first is a hydrodynamic model that provides the velocity field and elevation of the water flow. The second is a advection-dispersion-reaction model that gives the pollutant concentration fields after input of the velocity data from the hydrodynamic model. For numerical techniques, we used the Crank-Nicolson method for system of a hydrodynamic model and the explicit schemes to the dispersion model. The revised explicit schemes are modified from two computation techniques of uniform flow stream problems: forward time central space (FTCS) and Saulyev schemes for dispersion model. A comparison of both schemes regarding stability aspect is provided so as to illustrate their applicability to the real-world problem.

Numerical Simulations of Water Quality Measurement Model in an Opened-Closed Reservoir with Contaminant Removal Mechanism

“…The Lax-Wendroff method involves starting to calculate a first half step and then using the result from the half step to calculate the full step [7,8]. To find the water velocity and water elevation, we now discretize (2) on a rectangle reservoir with length and width .…”

“…, in which , , and are positive integers. Using the Lax-Wendroff method [7,8] on (2), we can obtain the following finite difference equation of hyperbolic partial differential equations.…”

“…In [5], the method of the characteristic technique combined with Galerkin finite element method is used to solve the shallow water mass transport problems. In [6,7], the numerical techniques are used to solve the nonuniform flow of stream water quality model with the advection-dispersionreaction equations. In [8], the Crank-Nicolson method is used to solve the hydrodynamic model and the backward time central space (BTCS) for the dispersion model.…”

A numerical treatment of a non-dimensional form of a water quality model in the Rama-nine reservoir

“…In [3], [8], [13], [14], [15] and [16], the finite element method for solving steady and unsteady water pollution measurements are presented. The various numerical techniques to solve the uniform flow of stream water quality model are presented in [5], [11] and [12].The numerical methods to approximate the solution of the two-dimensional advection-diffusionreaction equation are proposed in [6][7][8][9][10].…”

“…The hydrodynamics model provides the velocity field and tidal elevation of the water. In [4][5][6][7][8][9][10][11][12], the hydrodynamics model and advection-diffusion equation were used to approximate the velocity of the water current in a bay and a channel. In [7,16], the results from hydrodynamic model are data for the non-uniform flow of the advection-diffusion-reactione quation, which provides the pollutant concentration field.…”