Study on the most suitable computational method for diffusion numerical simulation

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1. Taking into account the highly accurate and stable features of the finite difference of second order derivative, the new refined scheme for advection is developed based on the concept of solving 2nd order wave equation instead of 1st order advection equation. Characteristics method is used in order to get an accurate solution propagating downstream only. From Taylor series analysis and many numerical experiments, parameters involved in this method could be determined as functions of Courant number. Comparison of this scheme with the other various ones in model calculations and Von Neumann stability analysis prove its superior accuracy and stability. This scheme can easily be applied to multidimensional practical problems by separating characteristic curve each component direction. This proposed scheme uses only three computational grid points, so that there is no need to pay much attention to the treatment at the boundary.2. On making accurately and effectively a numerical diffusion simulation, one should pay much attention to both the computational scheme for calculating the advection term and the computational grid size. The usable schemes for obtaining the high-accurate results depend on not only computational conditions such as grid intervals on time and space but also hydraulic conditions such as physical diffusion and velocity, while there will be the most effective grid size to get accurate solution within the allowable margin of error if the scheme used for the numerical simulation is chosen. We have attempted to develop a criterion for selecting the most usable scheme to calculate the advection term and deciding the most effective computational grid size. We made a 2nd order numerical diffusion term represent the truncation error terms, which is a infinite series. The criterion was made up by utilizing the 2nd order numerical diffusivity. Some one-dimensional test diffusion simulations have been carried out to inspect the validity of the criterion