High resolution schemes: total variation stability and its dependence on smoothness parameter
نویسنده
چکیده
A classi cation in terms of accuracy of ux limited high resolution schemes in steep gradient region is done based on two di erent total variation (TV) stability region. The dependence of TV stability region on the smoothness parameter is discussed which relates these two TV stability regions. A common unifying TV stability region is proposed for both class of schemes. Moreover new ux limiters, satisfying the unifying TV stability region are also proposed which are robust and work e ciently for both backward (left) and forward (right) moving solution pro le. Main signi cant feature of this work is that it can improve accuracy of all existing ux limiters based schemes. Numerical results on linear test problems are given to support the theoretical discussion.
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