Invariant solutions and submodels in two-phase fluid mechanics generated by 3-dimensional subalgebras: Barochronous flows

• Published in: International journal of non-linear mechanics 2019-11, Vol.116, p.140-146
• Main Author: Panov, A.V.
• Format: Article
• Language: English
• Subjects: Computational fluid dynamics; Fluid flow; Fluid mechanics; Group theory; Ideal fluids; Invariant solution; Invariants; Optimal system of subalgebras; Partially invariant submodel; Symmetry; Three dimensional flow; Three dimensional models; Two-phase fluid
• ISSN: 0020-7462; 1878-5638
• DOI: 10.1016/j.ijnonlinmec.2019.05.002

A model of two-phase isothermal ideal fluid is investigated by methods of the symmetry group theory. Different types of submodels are obtained for this model with respect to 3-dimensional subalgebras: invariant and partially invariant submodels. All invariant submodels are integrated. Ten subalgebras of the symmetry algebra are considered. Only these subalgebras generate barochronous motions of two-phase fluid. Many new exact solutions of two-phase fluid mechanics are found. They describe different motions of two-phase fluid, such as homogeneous motions, Galileo invariant motions and the motions with linear field of velocities. Two applications of the solutions are presented. •Two-phase fluid motions invariant under a 3-dimensional group action are considered.•Partially invariant submodels are obtained.•New examples of barochronous motions in a two-phase fluid are given.•Many new exact solutions of two-phase fluid mechanics are found.