本文研究目的在於如何利用數值方法，建立方便使用的虛擬東方毛筆繪圖模型。本文中採用省略壓力項之簡化二維不可壓縮奈威爾－史托克方程式(Navier－Stokes equation)計算水墨的運動，並依照毛筆幾何模型BGM（Brush Geometry Model），配合筆觸(Stroke)的運動軌跡，規範出筆觸範圍之後給予墨水源（Ink-water source）。在流場空間部分採用三階上風有限體積法，時間部分則是使用二階郎奇－庫達法（Two-step Runge-Kutta Method）來計算；此一模型以筆觸速度為主要流場變數，如此考量是為符合兼顧方便性，及計算速度的目標之考量。
　　參考目前應用於虛擬東方毛筆繪圖之硬體設備，本研究簡化需要控制的因素，使模型方面得以配合硬體之可能性。尤其在墨水源範圍規範方面，設定易於調整的毛筆幾何模型外，依據筆觸的運動軌跡，配合本文中之BMDM(Brush Motion Dynamic Model)裡的參數控制，以達到想要顯示的筆觸形狀。最後再依調整雷諾數、水量與染墨量之比例、沉澱係數，以及蒸發係數…等等，規劃出本文所希望呈現的墨韻效果，例如：擴散、吸收，以及黑邊效應等等。

This study aims to establish a handy Chinese brush model with numerical method. The simplified 2D incompressible Navier－Stokes equation with pressure term neglected is used for the calculation of the water-ink mixture motion. According to the BGM （Brush Geometry Model）and the stroke trajectory, ink-water sources are determined in the given stroke area. The third-order upstream finite volume method with two-step Runge-Kutta Method is used for the generation of flowfield grid. The stroke velocity is the key parameter in this model due to improve the calculation speed and to ensure convenience.
This study introduces the number of the controlled variables, such as , , , etc., to match the capability of the hardware for brush simulation available nowadays. Also establish an an easy-to-modulate brush model in the source area definition and the BMDM (Brush Motion Dynamic Model) variable control according to the brush motion trajectory to achieve the desired stroke geometry. The final ink diffusion effect, such as diffusion, dissipation and dark-edge effect, is modulated by adjusting Reynold’s number water-ink ratio, precipitation coefficient and vaporization coefficient.

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