Publication

An adaptive finite element method with crosswind diffusion for low Mach, steady, laminar combustion

2003
Journal Articles

Abstract

We investigate adaptive finite element methods for low Mach, steady, laminar combustion. The finite element discretization of the flame equations involves least squares control of streamline derivatives and pressure-velocity coupling as well as a new shock capturing term based on nonlinear crosswind diffusion yielding a suitable discrete maximum principle for the discrete solution. A posteriori error estimates derived from the dual weighted residual method are used to refine the mesh adaptively. Numerical results are presented for a Bunsen flame with simple chemistry on locally refined as well as fully unstructured Delaunay meshes. Solution quality is evaluated in terms of overall flame characteristics - including length, lift off and width - as well as undershoots in species and temperature profiles

Official source

https://infoscience.epfl.ch/entities/publication/30025bd4-a2b6-4264-a289-c28334f7fbe9

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2003
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/30025bd4-a2b6-4264-a289-c28334f7fbe9

About this result

Related concepts (32)

Finite element method

The finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).

Discretization

In applied mathematics, discretization is the process of transferring continuous functions, models, variables, and equations into discrete counterparts. This process is usually carried out as a first step toward making them suitable for numerical evaluation and implementation on digital computers. Dichotomization is the special case of discretization in which the number of discrete classes is 2, which can approximate a continuous variable as a binary variable (creating a dichotomy for modeling purposes, as in binary classification).

Numerical analysis

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.

Related publications (32)

An adaptive finite element method with crosswind diffusion for low Mach, steady, laminar combustion

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