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CGCircuit - Building Fluid Solvers for VFX and Houdini- Part 1&2

为 VFX 和 Houdini 构建流体求解器教程。

第一部分：

第一章：微分学

我们将从微积分1的基础知识开始。什么是函数？什么是导数？我们如何计算它们？我们将通过大量示例讲解常用的微分技巧。

第二章：积分学

我们将介绍积分作为微分的逆过程，并练习模拟物理中所需的多种积分技巧。

第三章：多元微积分与模拟核心数学

这才是真正开始的地方。您将学习如何对多元函数进行微分和积分，我们将探索流体模拟中最基本的导数算子：

梯度

散度

旋度

拉普拉斯算子

……等等。

我们还将介绍您需要用到的线性代数概念——不会太深奥，只讲解对您的求解器至关重要的内容。

重要提示：

构建像 Houdini 或 RealFlow 这样功能齐全的求解器需要多年的研发和庞大的开发团队。本课程并非旨在复制现有课程，而是为您提供进入该领域的钥匙。无论您是想编写自己的仿真工具、更好地理解求解器的工作原理，还是想成长为一名优秀的FX技术总监，本课程都是您的第一步。

第二部分：

第一章：常微分方程、偏微分方程和矩阵 了解仿真中使用的方程类型——常微分方程和偏微分方程——以及线性代数和矩阵如何支持它们。

第二章：流体方程 以简明易懂的方式探索著名的纳维-斯托克斯方程。了解它们的推导过程以及它们与现实世界流体行为的关系。我们还将介绍边界条件。

第三章：MAC网格和离散化 学习如何对空间和时间进行离散化以进行仿真。我们将重点介绍广泛应用于流体求解器的标记单元（MAC）网格技术。

第四章：平流技术 深入研究流体模拟中的平流步骤。您将了解半拉格朗日方法、其简洁性以及缺点（例如人工扩散）。

第五章：强制不可压缩性 这是构建真实流体的核心！学习如何应用不可压缩性条件、求解由此产生的线性方程组以及有效地处理边界条件。

第六章：Houdini 中的简易烟雾求解器 亲眼见证所有理论的实际应用。您将使用 Houdini 的 DOP 微求解器构建一个简单的烟雾求解器，将理论转化为实际的工作流程——这是编写您自己的求解器代码之前必不可少的一步。

Part 1 : 

Chapter 1: Differential Calculus

We’ll begin with Calculus 1 basics. What is a function? What’s a derivative? How do we compute them? We’ll go through common differentiation techniques with plenty of examples.

Chapter 2: Integral Calculus

We’ll cover integration as the reverse process of differentiation, and practice multiple integration techniques needed in simulation physics.

Chapter 3: Multivariable Calculus & Core Math for Simulations

This is where things get real. You’ll learn how to differentiate and integrate multivariable functions, and we’ll explore the most essential derivative operators in fluid simulation:

Gradient

Divergence

Curl

Laplacian

...and more.

We’ll also introduce the linear algebra concepts you’ll need—nothing too advanced, just what matters for your solver.

Important Note:

Building a full-featured solver like Houdini or RealFlow takes years of R&D and a large development team. This course doesn’t aim to replicate that—but it gives you the keys to enter the field. Whether you want to write your own simulation tools, better understand how solvers work, or grow as an FX TD, this course is your first step.

Part 2 : 

Chapter 1: ODEs, PDEs, and MatricesUnderstand the types of equations used in simulations—ordinary and partial differential equations—and how linear algebra and matrices support them.

Chapter 2: Fluid EquationsExplore the famous Navier-Stokes equations in a simplified, approachable way. Understand how they are derived and how they relate to real-world fluid behavior. We also introduce boundary conditions.

Chapter 3: MAC Grids & DiscretizationLearn how to discretize space and time for simulation. We'll focus on the Marker-And-Cell (MAC) grid technique, widely used in fluid solvers.

Chapter 4: Advection TechniquesDive into the advection step of fluid simulations. You'll understand the Semi-Lagrangian method, its simplicity, and its drawbacks (like artificial diffusion).

Chapter 5: Enforcing IncompressibilityThis is the heart of realistic fluids! Learn how to apply the incompressibility condition, solve the resulting linear system, and handle boundary conditions effectively.

Chapter 6: Simple Smoke Solver in HoudiniSee everything in action. You'll build a simple smoke solver using Houdini's DOP microsolvers, translating the theory into practical workflows—an essential step before writing your own solver code.