Finite Volume Method: A Crash introduction

Finite Volume Method: A Crash introduction Before continuing, we want to remind you that this a brief introduction to the FVM. Let us use the general transport equation as the starting point to explain the FVM, We want to solve the general transport equation for the transported quantity in a givendomain, with given boundary conditions BC and initial conditions IC. This is a second order equation. For good accuracy, it is necessary that the order of the discretization is equal or higher than the order of the equation that is being discretized. By the way, starting from this equation we can write down the Navier-Stokes equations (NSE). So everything we are going to address also applies to the NSE. Let us use the general transport equation as the starting point to explain the FVM, Finite Volume Method: A Crash introductionProfile assumptions using Taylor expansions around point P(in space) and point t(in time) Hereafter we are going to assume that the discretization practice is at least second order accurate in space and time.

• The drawback of the limiters is that they reduce the accuracy of the scheme locally to first order, when (sharp gradient, opposite slopes). However, this is justify when it serves to suppress oscillations. • The various limiters have different switching characteristics and are selected according to the particular

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