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I have come across schemes where TVD (with flux limiters) is used for spatial discretisation along with Runge-kutta for Temporal discretisation.

Can TVD be used for Temporal discretisation? If so could you please point me to some references? I have been trying to look for it but couldn't find anything.

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  • $\begingroup$ You seem to already have the proper references. TVD is a time-evolution property of the entire numerical scheme. Gottlieb and Shu, for example, discuss the TVD property when applied to hyperbolic conservation laws discretized via the MOL. No PDE spatial or temporal discretization is TVD in its own right. $\endgroup$ – Spencer Bryngelson Dec 31 '18 at 23:29
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For SSP time integrators, a good reference is the book by Gottlieb, Ketcheson, and Shu

https://www.amazon.com/stability-preserving-runge-kutta-multistep-discretizations/dp/9814289264

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TVD is used only for spacial dicretization(as per my knowledge), using a TVD(total variation diminishing) scheme the total variation in a solution in transient state reduces over time.

It is a spacial discretization method that is intended to be stable(without 'wiggles'), and the variation in this system diminishes over time, it is not temporal discretization.

Also if you want to read on TVD 'An Introduction to Computational Fluid Dynamics' by H.K. Versteeg is good.

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