The equations governing the fluid dynamics are derived from the Navier–Stokes equation and can be described by the momentum and mass conservation equations:

where U,ρ,τ,p,g are the velocity [m/s], density [kg/m3], shear-rate tensor [kg/m/s2], pressure [Pa] and the gravitational vector [m/s2], respectively. The energy equation is given by

where a heat flux is assumed, defined by q=αeffe. The enthalpy [m2/s2], h is defined as the sum of the internal energy, e [m2/s2] and kinematic pressure pρ:

The third term in Equation (3) is the time derivative of the specific kinetic energy, which is given by K=|U2|/2. The last term in Equation (3), Stherm, is the thermal sink.

The transport of cisplatin was modeled as a passive scalar, governed by

where C is the concentration of cisplatin [mol/m3], D is the diffusion coefficient [m2/s] and Sc is the sink term for cisplatin [mol/m3/s]. The use of these general equations to describe dynamics in the peritoneal cavity, healthy tissue, viable tumor and necrotic core is explained in more detail below.

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