## AA 113: Aerospace Computational Science

Computational methods are pervasive in analysis, design and optimization of aerospace systems. This course introduces the fundamental concepts underlying aerospace computational science. Starting from the concepts of meshes, elements and point clouds, interpolation, quadrature and time integration, the techniques of finite difference, finite volume and finite element discretization of general PDE problems, and analysis of the accuracy, consistency and stability of discretized problems including treatment of boundary conditions are developed. In depth applications to computations of ideal subsonic, transonic and supersonic flows, and viscous internal and external flow with a turbulence model are introduced. Through the use of commercial and research software (ANSYS Fluent, SU2 and AERO Suite) the student is exposed to the use of computational tools for solving practical aerospace engineering problems. The course culminates with the treatment of multidisciplinary aerospace problems invol
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Computational methods are pervasive in analysis, design and optimization of aerospace systems. This course introduces the fundamental concepts underlying aerospace computational science. Starting from the concepts of meshes, elements and point clouds, interpolation, quadrature and time integration, the techniques of finite difference, finite volume and finite element discretization of general PDE problems, and analysis of the accuracy, consistency and stability of discretized problems including treatment of boundary conditions are developed. In depth applications to computations of ideal subsonic, transonic and supersonic flows, and viscous internal and external flow with a turbulence model are introduced. Through the use of commercial and research software (ANSYS Fluent, SU2 and AERO Suite) the student is exposed to the use of computational tools for solving practical aerospace engineering problems. The course culminates with the treatment of multidisciplinary aerospace problems involving coupling across more than one discipline, such as aero-thermal analysis (for hypersonic vehicle performance analysis or gas turbine blade cooling), fluid-structure interaction problems (such as flutter or flapping wing aeroelastic performance), and aeroacoustics (such as jet noise for next generation commercial supersonic transport or noise radiation from multi-rotor urban air mobility platform). Students are expected to pursue significant computational projects in two-person teams. nPrerequisites:
CME102,
CME104 (multivariable calculus, linear algebra, ODEs and some PDEs),
ENGR 14,
ME 30,
ME70, and Recommended courses:
AA102,
AA103.

Terms: Win
| Units: 3

Instructors:
Lele, S. (PI)

## BIOE 285: Computational Modeling in the Cardiovascular System (CME 285, ME 285)

This course introduces computational modeling methods for cardiovascular blood flow and physiology. Topics in this course include analytical and computational methods for solutions of flow in deformable vessels, one-dimensional equations of blood flow, cardiovascular anatomy, lumped parameter models, vascular trees, scaling laws, biomechanics of the circulatory system, and 3D patient specific modeling with finite elements; course will provide an overview of the diagnosis and treatment of adult and congenital cardiovascular diseases and review recent research in the literature in a journal club format. Students will use SimVascular software to do clinically-oriented projects in patient specific blood flow simulations. Pre-requisites:
CME102, ME133 and
CME192.

Terms: Win
| Units: 3

Instructors:
Marsden, A. (PI)
;
Nair, P. (TA)

## CME 102: Ordinary Differential Equations for Engineers (ENGR 155A)

Analytical and numerical methods for solving ordinary differential equations arising in engineering applications are presented. For analytical methods students learn to solve linear and non-linear first order ODEs; linear second order ODEs; and Laplace transforms. Numerical methods using MATLAB programming tool kit are also introduced to solve various types of ODEs including: first and second order ODEs, higher order ODEs, systems of ODEs, initial and boundary value problems, finite differences, and multi-step methods. This also includes accuracy and linear stability analyses of various numerical algorithms which are essential tools for the modern engineer. This class is foundational for professional careers in engineering and as a preparation for more advanced classes at the undergraduate and graduate levels. Prerequisites: knowledge of single-variable calculus equivalent to the content of
Math 19-21 (e.g., 5 on Calc BC, 4 on Calc BC with
Math 21, 5 on Calc AB with
Math 21). Placement diagnostic (recommendation non-binding) at:
https://exploredegrees.stanford.edu/undergraduatedegreesandprograms/#aptext.

Terms: Aut, Win, Sum
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Le, H. (PI)
;
Ali, F. (TA)
;
Ayala Bellido, C. (TA)
;
Lu-Yang, J. (TA)
;
Randall, S. (TA)

## CME 102ACE: Ordinary Differential Equations for Engineers, ACE

Students attend
CME102/ENGR155A lectures with additional recitation sessions; two to four hours per week, emphasizing engineering mathematical applications and collaboration methods. Prerequisite: students should submit application for enrollment at:
https://engineering.stanford.edu/students/programs/engineering-diversity-programs/additional-calculus-engineers before study list deadline. It is recommended students enroll in the regular section (
CME102) prior to submitting application.

Terms: Aut, Win
| Units: 6
| UG Reqs: GER:DB-Math, WAY-FR

## CME 104: Linear Algebra and Partial Differential Equations for Engineers (ENGR 155B)

Linear algebra: systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, LU factorization, eigensystem analysis, normal modes. Linear independence, vector spaces, subspaces and basis. Numerical analysis applied to structural equilibrium problems, electrical networks, and dynamic systems. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Applications in heat and mass transport, mechanical vibration and acoustic waves, transmission lines, and fluid mechanics. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications drawn from a variety of engineering fields. Prerequisite:
CME102/
ENGR155A.

Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)

## CME 285: Computational Modeling in the Cardiovascular System (BIOE 285, ME 285)

This course introduces computational modeling methods for cardiovascular blood flow and physiology. Topics in this course include analytical and computational methods for solutions of flow in deformable vessels, one-dimensional equations of blood flow, cardiovascular anatomy, lumped parameter models, vascular trees, scaling laws, biomechanics of the circulatory system, and 3D patient specific modeling with finite elements; course will provide an overview of the diagnosis and treatment of adult and congenital cardiovascular diseases and review recent research in the literature in a journal club format. Students will use SimVascular software to do clinically-oriented projects in patient specific blood flow simulations. Pre-requisites:
CME102, ME133 and
CME192.

Terms: Win
| Units: 3

Instructors:
Marsden, A. (PI)
;
Nair, P. (TA)

## EE 101B: Circuits II

Continuation of
EE101A. Introduction to circuit design for modern electronic systems. Modeling and analysis of analog gain stages, frequency response, feedback. Filtering and analog to digital conversion. Fundamentals of circuit simulation. Prerequisites:
EE101A,
EE102A. Recommended:
MATH 53 or
CME102.

Terms: Spr
| Units: 4
| UG Reqs: GER:DB-EngrAppSci, WAY-SMA

Instructors:
Murmann, B. (PI)

## ENGR 155B: Linear Algebra and Partial Differential Equations for Engineers (CME 104)

Linear algebra: systems of algebraic equations, Gaussian elimination, undetermined and overdetermined systems, coupled systems of ordinary differential equations, LU factorization, eigensystem analysis, normal modes. Linear independence, vector spaces, subspaces and basis. Numerical analysis applied to structural equilibrium problems, electrical networks, and dynamic systems. Fourier series with applications, partial differential equations arising in science and engineering, analytical solutions of partial differential equations. Applications in heat and mass transport, mechanical vibration and acoustic waves, transmission lines, and fluid mechanics. Numerical methods for solution of partial differential equations: iterative techniques, stability and convergence, time advancement, implicit methods, von Neumann stability analysis. Examples and applications drawn from a variety of engineering fields. Prerequisite:
CME102/
ENGR155A.

Terms: Spr
| Units: 5
| UG Reqs: GER:DB-Math, WAY-FR

Instructors:
Khayms, V. (PI)

## ME 285: Computational Modeling in the Cardiovascular System (BIOE 285, CME 285)

This course introduces computational modeling methods for cardiovascular blood flow and physiology. Topics in this course include analytical and computational methods for solutions of flow in deformable vessels, one-dimensional equations of blood flow, cardiovascular anatomy, lumped parameter models, vascular trees, scaling laws, biomechanics of the circulatory system, and 3D patient specific modeling with finite elements; course will provide an overview of the diagnosis and treatment of adult and congenital cardiovascular diseases and review recent research in the literature in a journal club format. Students will use SimVascular software to do clinically-oriented projects in patient specific blood flow simulations. Pre-requisites:
CME102, ME133 and
CME192.

Terms: Win
| Units: 3

Instructors:
Marsden, A. (PI)
;
Nair, P. (TA)

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