Derivation of the method of characteristics for the fluid dynamic solution of flow advection along porous wall channels

This paper describes in detail a novel formulation of the method of characteristics for its application to solve one-dimensional compressible unsteady non-homentropic flow advected along porous wall channels. In particular, the method is implemented into a wall-flow monolith Diesel particulate filter model whose purpose is the pressure drop prediction. The flow inside the monolith channels is considered to be one-dimensional and the flow through the porous wall treated as a source term agree with the Darcy’s law. The flow dynamic behaviour at internal nodes of the channels is solved by means of shock capturing methods, whereas the end nodes, or boundary conditions, are solved applying the method of characteristics. The derived solution in this study of the Riemann variables and the entropy level includes the variation along the space–time plane due to cross-section area changes, friction and heat transfer as traditionally stated, but also takes into account the key influence on every line of the flow leaving or entering to the channels through the porous walls.