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Lecture

Convection: Numerical Flow Simulation

In course

ME-474: Numerical flow simulation

This course provides practical experience in the numerical simulation of fluid flows. Numerical methods are presented in the framework of the finite volume method. A simple solver is developed with Matlab, and a commercial software is used for more complex ...

Description

This lecture covers different discretization schemes for steady convection-diffusion problems, such as upwind differencing, linear upwind differencing, and quadratic upstream interpolation. It explains the concepts of boundedness, transportiveness, and conservativeness, as well as the accuracy and stability of each scheme. The lecture also introduces the deferred correction approach to handle negative coefficients and discusses the MUSCL scheme for unstructured meshes. Additionally, it presents the total-variation diminishing (TVD) schemes to achieve higher-order accuracy without introducing new extrema.

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Instructor

Edouard Boujo

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Related concepts (28)

Convection

Convection is single or multiphase fluid flow that occurs spontaneously due to the combined effects of material property heterogeneity and body forces on a fluid, most commonly density and gravity (see buoyancy). When the cause of the convection is unspecified, convection due to the effects of thermal expansion and buoyancy can be assumed. Convection may also take place in soft solids or mixtures where particles can flow. Convective flow may be transient (such as when a multiphase mixture of oil and water separates) or steady state (see Convection cell).

Transport

Transport (in British English) or transportation (in American English) is the intentional movement of humans, animals, and goods from one location to another. Modes of transport include air, land (rail and road), water, cable, pipelines, and space. The field can be divided into infrastructure, vehicles, and operations. Transport enables human trade, which is essential for the development of civilizations.

Convection–diffusion equation

The convection–diffusion equation is a combination of the diffusion and convection (advection) equations, and describes physical phenomena where particles, energy, or other physical quantities are transferred inside a physical system due to two processes: diffusion and convection. Depending on context, the same equation can be called the advection–diffusion equation, drift–diffusion equation, or (generic) scalar transport equation.

Stability theory

In mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.

Mode of transport

Mode of transport is a term used to distinguish between different ways of transportation or transporting people or goods. The different modes of transport are air, water, and land transport, which includes rails or railways, road and off-road transport. Other modes of transport also exist, including pipelines, cable transport, and space transport. Human-powered transport and animal-powered transport are sometimes regarded as their own mode, but never fall into the other categories.

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Transport Equations: Convection and Diffusion

Explores transport equations, emphasizing conservation principles and scheme stability.

Diffusion-Convection: Modeling and Schemes

Covers modeling and numerical schemes for diffusion-convection problems.

Diffusion and Convection Transport

Explores the microscopic description of diffusion and convection transport, emphasizing similarities between chemical diffusion and heat conduction.

Untitled

Convection-Diffusion: Boundary Layer Analysis