Multitemperature compaction model of a magma melt in the asthenosphere: A numerical approach

A numerical compaction model of a fluid in a viscous skeleton is developed with regard for a phase transition. The temperatures of phases are different. The solution is found by the method of asymptotic expansion relative to the incompressible variant, which removes a number of computational problems related to the weak compressibility of the skeleton. For each approximation, the problem is solved by the finite element method. The process of 2-D compaction of a magmatic melt in the asthenosphere under a fault zone is examined for one-and two-temperature cases. The magmatic flow concentrates in this region due to a lower pore pressure. Higher temperature magma entering from lower levels causes a local heating of the skeleton and intense melting of its fusible component. In the two-temperature model, a magma concentration anomaly develops under the fault zone. The fundamental limitations substantially complicating the corresponding calculations within the framework of a one-temperature model are pointed out and the necessity of applying a multitemperature variant is substantiated.