Abstract
The article discusses pressureless flows for filtration with a limiting pressure gradient. In the plane of the hodograph of the filtration rate, the search for the stream function reduces to the solution of a boundary-value problem for an elliptical equation in a region with curvilinear boundaries. A numerical solution of this problem is constructed by the method of finite elements, after which the whole picture of the flow is reconstructed by integration. An analysis is made of the effect of a limiting gradient on the integral characteristics of the flow. The fundamental special characteristics of problems of pressureless filtration in the presence of a limiting gradient are noted: the nonsingularity of the solution, the formation of stagnant zones adjacent to the free surface, etc.
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