A parallel implementation of a method of the semi-Lagrangian type for the advection equation on a hybrid architecture computation system is discussed. The difference scheme with variable stencil is constructed on the base of an integral equality between the neighboring time levels. The proposed approach allows one to avoid the Courant-Friedrichs-Lewy restriction on the relation between time step and mesh size. The theoretical results are confirmed by numerical experiments. Performance of a sequential algorithm and several parallel implementations with the OpenMP and CUDA technologies in the C language has been studied.

The analysis of ventilation systems effect on the main parameters of thermal conditions (temperature and velocity of air mass movement) of the working area in the premises heated by a gas infrared heater (GIH) was made by numerical simulation. The specific zones of the working area are considered in detail. The main regularities of temperature field changes in the total volume of the premises and local zones of working area in the case of relatively small air exchange made by ventilation system have been established.

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The paper demonstrates different ways of using the semi-Lagrangian approximation depending on the fulfillment of conservation laws. A one-dimensional continuity equation and a parabolic one are taken as simple methodological examples. For these equations, the principles of constructing discrete analogues are demonstrated for three different conservation laws (or the requirements of stability in the related discrete norms similar to the L1, L2, L∞-norms). It is significant that different conservation laws yield difference problems of different types as well as different ways to justify their stability.