Fluid Flow: Characteristics of PDEs and Discretization methods in CFD

Fluid Flow: Characteristics of PDEs and Discretization methods in CFD

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Mechanical Engineering

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Why enroll

People enroll in a course on Computational Techniques for PDEs to learn how to solve complex physical problems that cannot be tackled analytically. This course provides essential skills in numerical methods, discretization techniques, and stability analysis, which are critical for simulations in engineering, physics, and applied mathematics. Students gain practical knowledge in developing and implementing algorithms that are widely used in industries such as aerospace, energy, and climate modeling, making the course valuable for both academic research and professional applications.

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SPM & Welding Fixture Designer

AAAS Industries

Pantnagar , Uttarakhand

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Course details

Computational techniques for partial differential equations (PDEs) focus on converting continuous mathematical models into discrete forms that can be solved numerically. Discretization methods such as the finite difference, finite volume, and finite element methods break down spatial and temporal domains into smaller, manageable units, allowing PDEs to be approximated using algebraic equations. A key aspect of these methods is stability analysis, which ensures that numerical solutions remain accurate and bounded over time. Techniques like the Von Neumann stability analysis help determine whether errors will grow or dissipate during simulations. Mastery of these concepts is crucial for developing reliable and efficient computational models used in fields such as fluid dynamics, heat transfer, and structural mechanics.

Course suitable for

Aerospace
Automotive
Mechanical

Key topics covered

- Classification of Fluid Flow PDEs

- Characteristics of PDEs: Elliptic, Parabolic & Hyperbolic PDEs

- Key aspect of discretization in CFD

- Brief introduction to different methods of discretization: FDM & FVM

Course content

The course is readily available, allowing learners to start and complete it at their own pace.

Computational Techniques for PDEs: Discretization and Stability Analysis

1 Lectures

63 min

Lecture 01
63 min

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Mechanical Engineering