Direct Euler scheme

In this example the property tp is advanced using the explicit Euler scheme for all the operators. However, both implicit and explicit methods can be employed. In order to take a larger time steps, implicit methods are generally preferred. The convective and diffusive terms can be further split into their components in the various coordinate directions, for example, by use of the Strang [181] operator factorization scheme. 

Let us now discuss in detail the question of moment conservation during time integration. Consistently with Chapter 8, the source terms due to phase-space processes are set to zero so that only transport terms in real space are considered in this discussion. When Eq. (D.23) is integrated using an explicit Euler scheme, the volume-average moment of order k in the cell centered at X at time (n + l)Af is directly calculated from the volume-average moment of order k at time n Af from the following equation ... 

The gas-dynamics of the studied problem is described by a system of two-dimensional non-stationaiy Euler equations [87, 88]. The system is solved by the Lax-Wendroff scheme together with a flow correction algorithm for shock capturing. The detailed solution of the chemical reactions uses CHEMKIN-II and is included in the calculations. The solution domain consists of a half of a rectangular tube, divided into 400 X 200 cells. The spatial resolution in both x and y directions is uniform and equal to 0.3 mm. 

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