The convection term. Lagrangian and Eulerian calculations

Apart from including them in the equations, nothing has been said yet about the convective flux terms L. It is to these that attention is now directed. Including the modeling of flames stabilized on water-cooled burners, three distinct cases arise  

Pure Lagrangian computations use Eqs. (2.28) to (2.31) as the governing equations. The convective transfer terms are zero everywhere, that is, G, L +, and L are zero in the finite-difference equations 

Convergence to a steady rate of propagation may be monitored by the approach of the space integral rate over the whole flame to a constant value (cf. Section 2.6). The steady-state burning velocity My [or the product (M A)] may be obtained directly from Eq. (4.71) 

The pure Lagrangian approach without regridding has the theoretical advantage (over the Eulerian approaches to be described below) that it is 

In the Eulerian steady-state, stationary flame the time derivatives in Eqs. (4.12) and (4.13) become zero, and the computational problem becomes one of determining convective fluxes and flame profiles that will allow this to occur everywhere. 

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