This thesis consists of two parts. In the first part, nontrivial generalizations of the transport-collapse scheme are presented. The initial value problem for heterogeneous scalar conservation laws is considered and as a consequence of the analysis of the scheme a new solution concept of the initial-boundary value problem for scalar conservation laws arose. This is the most important contribution of this part of the thesis. In the both situations under the consideration the rigorous proofs of the convergence of the numerical scheme are given. In the last two chapters two models of fluid flows in different environments are presented. The first one models slow flows of two immiscible fluids with the source term put in the context of water pollution. Using the second model, the analysis of the evolution of the interface between immiscible fluids of different densities in porous media, is performed. The fluids can be compressible (\(CO_2\) or natural gases) or incompressible (oil, water). It is proven that, if the heavier fluid is on top and there is no sink or source term, a tip of the interface will move in the direction of the gravity or the buoyancy. In both situations, the appropriate numerical simulations are given.