Understanding the MC flux limiter

Context: Graduate
Thread starter nicksauce
Start date Aug 26, 2013
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Flux

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SUMMARY

The discussion focuses on the monotonized central difference (MCD) flux limiter used in numerical hydrodynamics. The formula presented involves calculating the flux at a grid point using a minimum of three terms, which include derivatives of the variable 'a' at neighboring points. The confusion arises from the interpretation of the terms, where the first term represents a standard derivative, while the subsequent terms are scaled derivatives, effectively ensuring stability and accuracy in the numerical scheme.

PREREQUISITES

Understanding of numerical hydrodynamics concepts
Familiarity with finite difference methods
Knowledge of flux limiters in computational fluid dynamics
Basic calculus, specifically derivatives

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Research the implementation of the MCD flux limiter in computational fluid dynamics simulations
Study the stability criteria for numerical methods in hydrodynamics
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Researchers and practitioners in computational fluid dynamics, numerical analysts, and anyone involved in the development of hydrodynamic simulation software.

Aug 26, 2013

nicksauce

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I'm reading through these notes on numerical hydrodynamics. On pg17, they introduce the monotonized central difference flux limiter, which looks something like

\frac{\partial~a}{\partial~x}|_i = min\left({\frac{|a_{i+1}-a_{i-1}|}{2\Delta~x},2\frac{|a_{i+1}-a_{i}|}{\Delta~x},2\frac{|a_i-a_{i-1}|}{\Delta~x}}\right)sign\left(a_{i+1}-a_{i-1}\right)

Now I am a bit confused about what's happening here. The first term in the min looks like a derivative, but the next two terms look like twice the derivative. Can anyone explain what exactly is going on here?

Thanks