Fluid Modeling of Plasmas

Course Date: March 13th – May 22nd, 2018
Lecture Time: 9:30am to 11:30am PT (Pacific Time)
Registration Fee: $650 (Regular), $325 (Student)
Early Bird Rate: $550 (Regular), $275 (Student)
Early Bird Deadline: February 6th, 2018
20% discount to former students!
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In 2018, we offered a new course on fluid modeling of plasmas. The syllabus is posted below. The goal is to teach you how to develop simulation codes based on the fluid model. Just as with aerodynamics, we can treat plasmas as a collection of kinetic particles (PIC) or as a fluid (MHD). As you learned in PIC Fundamentals, the fluid approach is appropriate when we can assume the velocity distribution function to be Maxwellian. Such is the case when density is high. In those instances, the kinetic approach would be prohibitively computationally expensive, and in the end would recover the same results as a fluid solver. In the course we will focus on a single and multi-species MHD description, but will also learn about hybrid approaches for coupling fluid electrons with kinetic ions. We will also cover some advanced topics such as fluid particle approach and Vlasov solvers.

Course Objectives

At the conclusion of this six lecture online course, you should understand how to derive the MHD equations and be able to develop your own MHD solver.

Course Format

In this course we will try something new, and will hold the lessons bi-weekly to give you more time to complete assignments. This should also give me more to get course materials ready. The course consists of sessions conducted through Citrix® GoToMeeting. The lectures will take place Tuesdays (tentative) from 9:15 to 11:45am US Pacific Time (GMT-8 hours). Participation in the live lectures is not required but is highly recommended. All registered students will receive access to a student area where the course materials will be posted. These materials will include recordings of the lectures, copy of the lesson slides, as well as the example codes. The course will also include optional weekly homework assignments, which will need to be completed in order to receive a certificate of completion.

Course Outline

  • March 13th, 2018 (Fluid formulation and Numerical Methods): We start the course by deriving the Navier Stokes and magnetohydronamic (MHD) fluid equations. We then review various methods for solving the advection-diffusion equation, which is a good model for the fluid equations.
  • March 27th, 2018 (Single fluid equation): We will spend this lecture developing solver that solve a single plasma fluid equation.
  • April 10th, 2018 (Multiple species MHD): Next we develop code that treats ions and electrons using their own MHD equations.
  • April 24th, 2018 (Hybrid PIC): We review the PIC method and develop a hybrid code that uses a detailed electron fluid model and compare results to the Boltzmann relationship from PIC Fundamentals
  • May 8th, 2018 (SPH and Fluid Particle model): The last two lectures will be on advanced topics. In this lecture we’ll review the Smoothed Particle Hydrodynamics (SPH) method before reviewing methods which attempt to combine the Lagrangian and Eulerian description of fluids.
  • May 22nd, 2018 (Vlasov Solvers): We close the course with a lecture on Vlasov solvers. These codes occupy an intermediary space between particle and fluid approaches since they solve a fluid-like equation, but the unknown is the distribution function (kinetic).


The instructor, Dr. Lubos Brieda, is the founder and president of Particle In Cell Consulting, LLC, a Los Angeles-based company specializing in providing tools and services for the plasma physics and rarefied gas communities. Dr. Brieda has over 10 years of experience developing PIC codes for a wide range of applications, including electric propulsion, space environment interactions, surface processing, and plasma medicine. His teaching experience includes the position of a Lecturer at the George Washington University.


Completion of the PIC Fundamentals course, or an existing understanding of the Particle In Cell (PIC) method, including particle motion, mesh interpolation, and field solving. In addition, all students are expected to have a basic understanding of numerical techniques, plasma and gas dynamics, and computer programming. The lectures and demonstration programs will utilize the C++ programming language. Students need to have access to a computer with a compiler of choice. The course will be conducted in English.

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