HROMADKA: CFD COURSE LECTURE CORE CONTENT:

HROMADKA: CFD COURSE LECTURE CORE CONTENT:

LESSON PLAN:
PART 2: ONE HOUR, TO END OF CLASS. CONTINUE IN SECOND LECTURE DAY.

The core CFD notes are found in the link below.
Because we are now focusing on CFD and using climate/weather as an application of CFD (as is using HEC-RAS !!!), then with the expanded time frame I suggest we target lectures 1, 2, 3, 6, 7, 16 and 20 with lectures 6 and 7 being if time permits in Day 2, and lecture 20 being mathematics background, but worth review. That review of math should reinforce the utility and motivation for keeping the math in their minds.

Lecture Notes from Andre Bakker (with Permission)

DEMONSTRATIONS:

Landslide into lake and resulting displacement wave

LECTURE CONTENT: SKIP IF BOSTON UNIVERSITY LECTURE NOTES ARE EXAMINED…
Good Original INTRO to CFD

Lecture Abbreviations and Terms:

Grid system algorithmic routines

Delaunay triangulation

DAE = Differential Algebraic Equations

IBVP = Initial Boundary Value Problem

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The scope of this book is to discuss recent numerical and algorithmic tools for the solution of certain flow problems arising in Computational Fluid Dynam ics (CFD). Here, we mainly restrict ourselves to the case ofthe incompressible Navier-Stokes equations, Ut – v~u + U . V’u+ V’p = f , V’·u = o. (1)…

Page 20
… a very efficient direct solver for stationary incompressible Navier–Stokes equations in 2D and 3D can be constructed … of Pressure Schur Complement solvers (local MPSC) we skip a more detailed explanation and refer to the next chapter.

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VIDEO LECTURE OF CFD MODELING CREDIBILITY: CFD BEHIND THE SCENES

NECESSARY MATHEMATICS TO ADVANCE WORK IN CFD; (END-USERS CAN OPERATE CFD COMPUTER MODELS)

• SOLVING SYSTEMS OF LINEAR EQUATIONS: SOLVING MATRIX SYSTEMS
• ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
• LAPLACE TRANSFORMS
• VECTOR MECHANICS: GREEN’S, STOKES, DIVERGENCE THEOREMS
• NUMERICAL METHODS: FINITE DIFFERENCE, FINITE ELEMENT, BOUNDARY ELEMENT, COMPLEX VARIABLE BOUNDARY ELEMENT
•FOURIER SERIES
•PROBABILITY AND STATISTICS — COMPUTATIONAL ERROR ANALYSIS AND SENSITIVITY QUANTIFICATION

EXAMPLE UNIVERSITY PROGRAMS:

Stanford School of Earth, Engergy & Environmental Sciences

Computational Geoscience

CompGeo Requirements

The M.S. CompGeo track is offered through the Institue for Computational Mathematics and Engineering. For more information about the requirements and admissions process please see the ICME website.
Students are required to take 45 units of coursework, and research credits to earn an M.S. in CompGeo. The coursework follows the requirements of the traditional ICME M.S. degree with additional restrictions placed on the general and focused electives. As defined in the general Graduate Student Requirements students have to maintain a grade point average (GPA) of 3.0 or better and must be taken at the 200 level or higher. In order to continue on to the Ph.D. in ICME M.S. students have to maintain at a GPA of at least 3.5.

Requirement 1: Foundational

Students must demonstrate foundational knowledge in the field by completing the courses in two of the three core parts:

 

Courses in this area must be taken for letter grades. Deviations from the core curriculum must be justified in writing and approved by the student’s ICME adviser and the chair of the ICME curriculum committee. Courses that are waived may not be counted towards the master’s degree.

Requirement 2: Breadth Electives in Computational Geoscience

The M.S. CompGeo track requires 18 units of course work in the Geosciences (3 units can be applied from a non-computationally focused course). Courses are currently offered but are not limited to the following specific areas of the School of Earth Sciences:

1. Reservoir Simulation
2. Geophysical Imaging
3. Tectonophysics/Geomechanics
4. Climate/Atmosphere/Ocean
5. Ecology/Geobiology

The Earth Science courses, offered in EESS, ERE, GES, and Geophysics is selected based on the area of the student’s interest and their research/thesis work, along with the advice and consent of the student’s adviser. Students are encouraged to choose a range of courses in order to guarantee breadth of knowledge in Earth Sciences. A maximum of one non-computationally-oriented course can be counted towards the master’s degree requirements. A list of courses that fulfill this requirements is available at Course Listings.

Requirement 3: Integrative Research in Computational Geoscience

9 units of focused research in computational geoscience. Students are required to either complete a Research Project or an Internship as described below.

Research Project

Students who plan to apply to the Ph.D. program need to take 9 units of research. Students will work with the CompGeo program director to find an appropriate advisor and research topic and then enroll in EARTHSCI 400:Directed Research (or a similar SES research course). The successful outcome of a Research Project can be:

1. an oral presentation at an international meeting requiring an extended abstract
2. a publication submission in a peer reviewed journal.
3. a written report

Internship

As an alternative to the Research Project students have the option of an internship which is recommended for those students interested in a terminal degree. The individual student is responsible for securing and organizing the internship and is required to obtain a faculty advisor and submit a written report on the internship project. Credit for the internship will be obtained through EARTHSCI 401: Curricular Practical Training (1 unit) and in this case only 8 units of research are required.

Requirement 4: Programming

3 units of programming course work demonstrating programming proficiency. All graduate students in the program are required to complete programming course at the level of CME 212 or higher.

Requirement 5: Seminar

3 units of ICME graduate seminars or other approved seminars. Additional seminar units may not be counted towards the 45-unit requirement.One of the required seminars for CompGeo must be EARTHSCI 310 Computational Geosciences Seminar (1 unit).

Fundamentals:

Note:
Fundamental courses in mathematics and computing may be needed as prerequisites for other courses in the program. Check the prerequisites of each required course. Preparatory courses include such subjects as: calculus, linear algebra and differential calculus of several variables, integral calculus of several variables, ODEs with linear algebra, linear algebra and matrix theory, vector calculus for engineers, linear algebra and PDEs for engineers, introduction to scientific computing, linear algebra with application to engineering computations, PDEs in engineering, Computer Programming in C++ for Earth Scientists and Engineers, Introduction to Large-Scale Computing in Engineering, numerical linear algebra, programming methodology, programming abstractions, machine learning, introduction to optimization, theory of probability, and data mining and analysis.

Computational Geoscience

397 Panama Mall
Stanford, CA 94305-2210

THERE ARE SEVERAL ESTABLISHED AND EMERGING PROGRAMS

About PACM
PACM (the Program in Applied and Computational Mathematics) is an interdisciplinary and interdepartmental program that provides a home for people from many fields and directions, who share a passion for mathematics and its applications.

Our core faculty is presently constituted by 12 core faculty members who hold a joint appointment between their home department and PACM; the faculty also function as an executive committee for PACM in all its important decisions.

Drawing from a wide range of departments, from the physical sciences and engineering to the human sciences, PACM counts 51 Princeton faculty members among its associate faculty; they provide mentoring and advising to our students interested in their fields of expertise. We have both a graduate program and an undergraduate certificate program. Currently for the 2013-14 academic year, we have 25 graduate students enrolled and 45 undergraduate certificate students.

The Program in Applied and Computational Mathematics
Princeton University, Fine Hall
Washington Road, Princeton, NJ 08544-1000 USA
Phone: 609-258-3703

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