Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Diffusion-Convection: Modeling and Schemes

Description

This lecture covers the modeling and numerical schemes for diffusion-convection problems, focusing on explicit and implicit schemes. The instructor explains the concepts of diffusion-convection, boundary conditions, and stability criteria for different schemes.

Official source

Related concepts (32)

Chicken (Scheme implementation)

Chicken (stylized as CHICKEN) is a programming language, specifically a compiler and interpreter which implement a dialect of the programming language Scheme, and which compiles Scheme source code to standard C. It is mostly R5RS compliant and offers many extensions to the standard. The newer R7RS standard is supported through an extension library. Chicken is free and open-source software available under a BSD license. It is implemented mostly in Scheme, with some parts in C for performance or to make embedding into C programs easier.

Scheme (programming language)

Scheme is a dialect of the Lisp family of programming languages. Scheme was created during the 1970s at the MIT Computer Science and Artificial Intelligence Laboratory (MIT AI Lab) and released by its developers, Guy L. Steele and Gerald Jay Sussman, via a series of memos now known as the Lambda Papers. It was the first dialect of Lisp to choose lexical scope and the first to require implementations to perform tail-call optimization, giving stronger support for functional programming and associated techniques such as recursive algorithms.

Numerical stability

In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.

Data

In common usage and statistics, data (USˈdætə; UKˈdeɪtə) is a collection of discrete or continuous values that convey information, describing the quantity, quality, fact, statistics, other basic units of meaning, or simply sequences of symbols that may be further interpreted formally. A datum is an individual value in a collection of data. Data is usually organized into structures such as tables that provide additional context and meaning, and which may themselves be used as data in larger structures.

Big data

Big data primarily refers to data sets that are too large or complex to be dealt with by traditional data-processing application software. Data with many entries (rows) offer greater statistical power, while data with higher complexity (more attributes or columns) may lead to a higher false discovery rate. Though used sometimes loosely partly because of a lack of formal definition, the interpretation that seems to best describe big data is the one associated with a large body of information that we could not comprehend when used only in smaller amounts.

Related lectures (58)

Convection-Diffusion: Boundary Layer Analysis

Discusses boundary layer analysis in convection-diffusion problems, focusing on numerical schemes and stability.

Finite Difference Grids

Explains finite difference grids for computing solutions of elastic membranes using Laplace's equation and numerical methods.

Waves and Diffusion: Fundamentals

Covers the fundamentals of waves, diffusion, and convection, focusing on the concepts of propagation, initial conditions, and boundary conditions.

Computational Geomechanics: Week 4

Explores transient flow in porous media, covering governing equations, stability conditions, and numerical methods.

Advanced Numerical Analysis: Space Discretization