V. S. Borisov

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The paper is concerned with dynamics of multi-phase media consisting of a solid permeable material and a compressible Newtonian fluid. Governing macroscopic equations are derived starting from the space-averaged microscopic mass and momentum balances. The Reynolds stress models (i.e., momentum dispersive fluxes) are discussed, and a suitable model is(More)
In this paper, we focus on the application and illustration of the approach developed in part I. This approach is found to be useful in the construction of stable and monotone central difference schemes for hyperbolic systems. A new modification of the central Lax–Friedrichs scheme is developed to be of second-order accuracy. The stability of several(More)
Burn injury is accompanied by the formation of reactive oxygen species (ROS). Excessive production of ROS results in oxidative stress. Peroxidation damage of proteins causes their degradation and the formation of toxic fragments con- tributing to the development of endogenous intoxication. Furthermore, burns cause pronounced inflammatory reaction in the(More)
The monotonicity and stability of difference schemes for, in general, hyperbolic systems of conservation laws with source terms are studied. The basic approach is to investigate the stability and monotonicity of a non-linear scheme in terms of its corresponding scheme in variations. Such an approach leads to application of the stability theory for linear(More)