設計及發展有效的數值方法，以建立方便使用的虛擬東方毛筆繪圖模型即為本文之主要研究目的。於數值方法上，本研究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，規範出筆觸範圍後給予墨水源（Ink-water source）。在流場空間採用上風有限體積法，時間則是使用二階郎奇－庫達法（Two-step Runge-Kutta Method）計算；此模型以筆觸速度為主要流場變數，此考量是為符合兼顧方便性及計算速度之考量。
　　本研究簡化需要控制的因素，如使模型方面得以相互配合，達到以實際運筆所顯示的筆觸形狀。在墨水規範方面，除了易於調整的毛筆幾何模型，使用者亦可選擇自己喜好的顏色進行調配，此外，亦加入虛擬的紙張模型以增加其真實性；最終，依使用者需求設定參數且依據筆觸的運動軌跡，配合本文中之模型操作流程，即可完成書法作品及水墨畫作品。

This study aims to establish a handy 3D virtual Chinese-brush painting model coupled with a numerical method. The numerical method uses a simplified 2D Navier－Stokes equation with neglected pressure term to calculate motion of the water-ink mixture. According to the BGM （Brush Geometry Model）and trajectory of the stroke motion, ink-water sources are determined in the given stroke area. A upwind finite volume method coupled with a two-step Runge-Kutta time integration is used to solve the flow fields. The stroke velocity is the key parameter in this model that is due to improving the calculating flow speed and to adding the convenience.

　　This study simplifies the factors of the controlled variables, such let the painting model match up each model to come up with the shape of the stroke by real operation. We also include the models of the virtual papers to increase its authenticity. In addition to the easy-to-modulate brush model in the ink-water area, users can also choose any colors mixed by himself. Finally, users can finish calligraphic works and paintings by choosing parameters according to the demand of the users, trajectory of the stroke motion, and matches with operating procedures of this painting model in this paper.

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