以粒子為基礎的蠟燭融化模擬

Abstract

我們提出一個基於光滑粒子流體動力學法(Smoothed-Particle Hydrodynamics)來模擬蠟燭融化。藉由使用幽靈粒子(ghost particle)並且確保橫跨固體邊界的密度場是連續的，融化後的液體可以自然地沿著表面流動，而不需要使用人工的界面張力。除此之外，藉由設定特別的幽靈速度(ghost velocity)以及使用平均後的速度場(XSPH)，流體的附著度可由一個直覺的參數調整。為了模擬融化的過程，一個完整的熱傳導被提出。熱傳導系統不止模擬粒子間的熱流，還模擬了和環境的熱交換。相變包含了固體到液體以及液體到氣體，它的發生是由模擬出來的溫度所決定。我們分裂粒子來保留黏滯液體因流動所產生的線狀物。螢幕空間顯像被用來呈現模擬結果。為了捕捉輪廓鮮明且凸出的液滴形狀，本來用於代表一顆粒子的球被拉長成橢球。

We propose a SPH-based particle simulation for candle melting. By using ghost parti- cles and ensuring the continuous density field across the solid boundary, the melting liq- uids can flow along the surface naturally without applying artificial interfacial tension. Moreover, by setting specific ghost velocities and applying XSPH, the stickiness of the fluid can be controlled easily by an intuitive parameter. To simulate the melting process, a complete thermal transfer is proposed. The thermal transfer system simulates not only the heat flow between particles but also the heat exchange with the environment. Also, the occurrence of the phase transition, including solid-to-liquid and liquid-to-air, is de- termined by the simulated temperature. We split the particles to preserve the shape of thread formed by the flow of viscous liquid. Screen space point splatting method is applied to display the simulation result. The sphere originally used for representing the particle is stretched to the ellipsoid to capture the sharp and protruded shape of droplets.