Understanding Fluid Solvers – Volume 2 by MIX Training

# Understanding Fluid Solvers – Volume 2

In this second course in the series we will talk about fluids and how to simulate a fluid with equations which seems very hard but as promised, we will make things simple as possible.
In this second course in the series we will talk about fluids and how to simulate a fluid with equations which seems very hard but as promised, we will make things simple as possible. After that we will talk about how a simple smoke solver is implemented in Houdini with microsolvers. This is just a start point for you to start your code. We won't talk about a full code but simple smoke solver with microsolvers. After taking this course you can begin your code or learn without doubt of not understanding in this field. You will understand the core concepts that will make you able to go deeper and learn more about different techniques in a lot of paper on the Internet. Though, you will see an application in Houdini microsolvers.

Duration: 7 Hours 38 mins.

# Chapter 1 : ODEs, PDEs and matrices

We will talk about the kinds of equations we will use to describe fluids which are ODEs and PDEs. We will talk also about some linear algebra and matrix operations. # Chapter 2 : Fluid Equations

Here, you will see one of the coolest equations that a lot of people love ( though they are scary), Navier - Stokes Equations. We will learn how they are derived and more! All of this in simple ways. We will also talk about boundary conditions. # Chapter 3 : MAC Grids, discretization in time and space

Before you solve the equations, you should learn how to discretize different quantities in time and space. We will talk about an efficient way to discretize in space called MAC Grid. We will talk about efficient way to solve the advection part of our equations. Considering Semi Lagrangian scheme as the main way we will use,we will talk about artificial diffusion as a result of it. # Chapter 5 : Making fluid incompressible

This is the hear of fluid simulations! This chapter will contain a lot of information. We will talk about how to apply the incompressibility condition and satisfy boundary conditions. This will consider solving a linear system too. # Chapter 6 : Simple Smoke Solver.

Now it's time to see how all of this is applied in Houdini! We will see how a simple smoke solver is done with microsolvers. This is the best way to start coding your own code after learning all of these definitions and seeing how to apply in microsolvers. ### What's included?

1 video 43 files 1 text file

# Contents

00 - Fluid Solvers overview 02
5 mins
Community
1.1 - Introduction to PDEs and ODEs
1.2 - Some Linear Algebra
2.1 - Navier-Stokes Equations
2.2 - Lagrangian and Eulerian Viewpoints
2.3 - Material Derivative in vectors and Example
2.4 - Incompressibility Condition_title
2.5 - Dropping Viscosity
2.6 - Boundary Conditions
3.1 - What's numerical simulation
3.2 - Discretization in time
3.3 - Splitting Fluid Equations Part 1
3.4 - Splitting Fluid Equations Part 2
3.5 - Selecting the time step
3.6 - Taylor Series
3.7 - Finite Differencing
3.8 - MAC Grid
3.9 - Discretization in space
3.10 - Estimating Velocity on staggered grid
4.1 - Introduction to solving Advection Equation
4.2 - Semi-Lagrangian Approach
4.3 - Linear and Bilinear Interpolations
4.4 - Numerical Diffusion
4.5 - Final Notes on SL advection
5.1 - Introduction to Finite Difference Linear Systems
5.2 - Finite Differencing Linear Systems in 2D
5.3 - Discrete Pressure Introduction
5.4 - Discrete Pressure Part 2 Formulas
5.5 - Discrete Pressure Part 3 Boundaries
5.6 - Pressure Update Code
5.7 - Discrete Divergence
5.8 - Divergence Update Code
5.9 - Pressure Equations
5.10 - Update according to boundaries
5.11 - Introduction to line search methods
5.12 - Introduction to Conjugate Gradient Method
5.13 - Storing 5 , 7 stencil matrix
5.14 - Pseudo code for storing a matrix
5.15 - Final notes on CG
6.1 - Smoke Solver Example Introduction
6.3 - Time Steps
6.4 - Modified Smoke Solver In Depth
6.5 - What's next