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Motivated by the mathematical modeling of tumor invasion in healthy tissues,we propose a generalized compressible diphasic Navier-Stokes Cahn-Hilliardmodel that we name G-NSCH. We assume that the two phases of the fluid representtwo different populations of cells: cancer cells and healthy tissue. We includein our model possible friction and proliferation effects. The model aims to beas general as possible to study the possible mechanical effects playing a rolein the invasive growth of a tumor. In the present work, we focus on theanalysis and numerical simulation of the G-NSCH model. Our G-NSCH system isderived rigorously and satisfies the basic mechanics of fluids and thethermodynamics of particles. Under simplifying assumptions, we prove theexistence of global weak solutions. We also propose a structure-preservingnumerical scheme based on the scalar auxiliary variable method to simulate oursystem and present some numerical simulations validating the properties of thenumerical scheme and illustrating the solutions of the G-NSCH model.

Analysis and numerical simulation of a generalized compressible Cahn-Hilliard-Navier-Stokes model with friction effects