HOLA: a High-Order Lie Advection of Discrete Differential Forms With Applications in Fluid Dynamics
HOLA: a High-Order Lie Advection of Discrete Differential Forms With Applications in Fluid Dynamics
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HOLA：离散微分形式的高阶李平流及其在流体动力学中的应用
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发表时间：
2007
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通讯作者：
A. McKenzie
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作者：
A. McKenzie
李导数，以及一般的外微积分，在许多动力系统的优雅几何解释中无处不在。通过引入定义在微分形式上的Lie导数的离散框架，包括实现它的基于WENO的数值格式，我们将最近的趋势扩展到离散外微积分。通过对标量场和向量场(任意离散k形式)的平流，证明了该算子的有效性。以流体流动涡度的Lie平流为例，对流体质量密度守恒Lie平流在计算机图形学中的稳健自由表面流动进行了重要的讨论。
The Lie derivative, and Exterior Calculus in general, is ubiquitous in the elegant geometric interpretation of many dynamical systems. We extend recent trends towards a Discrete Exterior Calculus by introducing a discrete framework for the Lie derivative defined on differential forms, including a WENO based numerical scheme for its implementation. The usefulness of this operator is demonstrated through the advection of scalar and vector valued fields (arbitrary discrete k-forms) in a desirable intrinsic and metric independent fashion. Examples include Lie advection of fluid flow vorticity, and we conclude with a significant discussion on the conservative Lie advection of fluid mass density for robust free surface flows in computer graphics.