Abstract
A numerical study is presented of 1D advection-diffusion problems having singular source terms. The singular source terms are defined by a Dirac delta function. As a consequence, the solutions of such problems are not continuously differentiable. This lack of smoothness form an obstacle for numerical discretization, including amongst others order reduction. In this paper the standard finite volume approach is considered for which reduction from order two to order one occurs. Numerical example is included.
Keywords
Discretization
Differentiable function
Dirac delta function
Advection
Numerical diffusion
Smoothness
Mathematics
Diffusion
Numerical analysis
Mathematical analysis
Reduction (mathematics)
Finite volume method
Applied mathematics
Function (biology)
Geometry
Physics
Mechanics
Subject Areas
Advanced Numerical Methods in Computational Mathematics
·Computational Mechanics ·Physical Sciences
Computational Fluid Dynamics and Aerodynamics
·Computational Mechanics ·Physical Sciences
Electromagnetic Simulation and Numerical Methods
·Electrical and Electronic Engineering ·Physical Sciences
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