Kinetics-based finite-volume methods

Appendix B. Kinetics-based finite-volume methods... 

To complete the book, four appendices are included. Appendix A contains the Matlab scripts for the most common moment-inversion algorithms presented in Chapter 3. Appendix B discusses in more detail the kinetics-based finite-volume methods introduced in Chapter 8. Einally, the key issues of PTC in phase space, which occurs in systems far from collisional equilibrium, and moment conservation with some QBMM are discussed in Appendix C and Appendix D, respectively. 

KBFVM kinetics-based finite-volume method... 

Thus, the study of two-phase flows in diffuser-confusor devices can provide us with reliable results, based on the interpenetrating continuum model (the Euler approach). The numerical solution of the partial derivatives of the differential equations in the C-e turbulence model, using the implicit integro-interpolation finite volume method, provides us with the following fields of functions for a diffuser-confusor reactor axial u and radial v rates for each of the phases pressure p volume fractions of continuous and dispersed phases specific kinetic energy of turbulence k and its dissipation s, as well as some other characteristics. 

It is apparent that as the momentum p increases, the finite difference spectrum deviates more and more from the correct value. It is usually assumed that acceptable accuracy with the FD method is obtained when at least 10 points are used per wave period. This means also using 10 points per unit volume in phase space. The finite difference algorithms are based on a local polynomial approximation of the wave function and therefore the convergence of the method follows a power law of the form (Aq)n, where n is the order of the finite difference approximation. This semilocal description leads to a poor spectral representation of the kinetic energy operator, which will be true as well, for other banded representations of the kinetic energy operator such as the... 

---