In this paper we proposed a modified Baer-Nunziato model for compressible multi-fluid flows,with main attention on the energy exchange between the two fluids.The proposed model consists of eleven PDEs;however,the use ...In this paper we proposed a modified Baer-Nunziato model for compressible multi-fluid flows,with main attention on the energy exchange between the two fluids.The proposed model consists of eleven PDEs;however,the use of the particular phase evolving variables may reduce the model to have only six PDEs.The main advantage of the model is that the Abgrall’s UPV criterion on mixture velocity and pressure is satisfied without affecting either its hyperbolicity or its conservations of the two individual masses,momentum or total energy.An Lax-Friedrichs scheme is built for a particular case of the proposed model.When the two fluids in the fluid mixture are both of the linear Mie-Gruneisen type,the scheme satisfies the Abgrall’s UPV criterion on mixture velocity and pressure.Numerical experiments with polytropic,barotropic,stiffened and van der Waals fluids show that the scheme is efficient and able to treat fluids characterized with quite different thermodynamics.展开更多
We investigate a version of one velocity Baer-Nunziato model with dissipation for the mixture of two compressible fluids with the goal to prove for it the existence of weak solutions for arbitrary large initial data o...We investigate a version of one velocity Baer-Nunziato model with dissipation for the mixture of two compressible fluids with the goal to prove for it the existence of weak solutions for arbitrary large initial data on a large time interval.We transform the one velocity Baer-Nunziato system to another"more academic"system which possesses the clear"Navier-Stokes structure".We solve the new system by adapting to its structure the Lions approach for solving the(mono-fluid)compressible Navier-Stokes equations.An extension of the theory of renormalized solutions to the transport equation to more continuity equations with renormalizing functions of several variables is essential in this process.We derive a criterion of almost uniqueness for the renormalized solutions to the pure transport equation without the classical assumption on the boundedness of the divergence of the transporting velocity.This result does not follow from the DiPerna-Lions transport theory and it is of independent interest.This criterion plays the crucial role in the identification of the weak solutions to the original one velocity Baer-Nunziato problem starting from the weak solutions of the academic problem.As far as we know,this is the first result on the existence of weak solutions for a version of the one velocity bi-fluid system of the Baer-Nunziato type in the mathematical literature.展开更多
In this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-con...In this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source terms.This scheme is constructed with a single stencil polynomial reconstruction operator,a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources,a nodal solver with relaxation to determine the mesh motion,a path-conservative integration technique for the treatment of non-conservative products and an a posteriori stabilization procedure derived from the so-called Multidimensional Optimal Order Detection(MOOD)paradigm.In this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become stiff.The new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence study.Classical Riemann problems and explosion problems with exact solutions are simulated in 2D and 3D.The overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.展开更多
基金supported by China National Science Foundation Grant No.10971132Leading Academic Discipline Project of Shanghai Municipal Education Commission No.J50101 and Shanghai Pu Jiang program[2006]118.
文摘In this paper we proposed a modified Baer-Nunziato model for compressible multi-fluid flows,with main attention on the energy exchange between the two fluids.The proposed model consists of eleven PDEs;however,the use of the particular phase evolving variables may reduce the model to have only six PDEs.The main advantage of the model is that the Abgrall’s UPV criterion on mixture velocity and pressure is satisfied without affecting either its hyperbolicity or its conservations of the two individual masses,momentum or total energy.An Lax-Friedrichs scheme is built for a particular case of the proposed model.When the two fluids in the fluid mixture are both of the linear Mie-Gruneisen type,the scheme satisfies the Abgrall’s UPV criterion on mixture velocity and pressure.Numerical experiments with polytropic,barotropic,stiffened and van der Waals fluids show that the scheme is efficient and able to treat fluids characterized with quite different thermodynamics.
文摘We investigate a version of one velocity Baer-Nunziato model with dissipation for the mixture of two compressible fluids with the goal to prove for it the existence of weak solutions for arbitrary large initial data on a large time interval.We transform the one velocity Baer-Nunziato system to another"more academic"system which possesses the clear"Navier-Stokes structure".We solve the new system by adapting to its structure the Lions approach for solving the(mono-fluid)compressible Navier-Stokes equations.An extension of the theory of renormalized solutions to the transport equation to more continuity equations with renormalizing functions of several variables is essential in this process.We derive a criterion of almost uniqueness for the renormalized solutions to the pure transport equation without the classical assumption on the boundedness of the divergence of the transporting velocity.This result does not follow from the DiPerna-Lions transport theory and it is of independent interest.This criterion plays the crucial role in the identification of the weak solutions to the original one velocity Baer-Nunziato problem starting from the weak solutions of the academic problem.As far as we know,this is the first result on the existence of weak solutions for a version of the one velocity bi-fluid system of the Baer-Nunziato type in the mathematical literature.
基金W.B.has been financed by the European Research Council(ERC)under the European Union’s Seventh Framework Programme(FP7/2007-2013)with the research project STiMulUs,ERC Grant agreement no.278267R.L.has been partially funded by the ANR under the JCJC project“ALE INC(ubator)3D”JS01-012-01the“International Centre for Mathematics and Computer Science in Toulouse”(CIMI)partially supported by ANR-11-LABX-0040-CIMI within the program ANR-11-IDEX-0002-02.The authors would like to acknowledge PRACE for awarding access to the SuperMUC supercomputer based in Munich,Germany at the Leibniz Rechenzentrum(LRZ).Parts of thematerial contained in this work have been elaborated,gathered and tested while W.B.visited the Mathematical Institute of Toulouse for three months and R.L.visited the Dipartimento di Ingegneria Civile Ambientale e Meccanica in Trento for three months.
文摘In this paper we present a 2D/3D high order accurate finite volume scheme in the context of direct Arbitrary-Lagrangian-Eulerian algorithms for general hyperbolic systems of partial differential equations with non-conservative products and stiff source terms.This scheme is constructed with a single stencil polynomial reconstruction operator,a one-step space-time ADER integration which is suitably designed for dealing even with stiff sources,a nodal solver with relaxation to determine the mesh motion,a path-conservative integration technique for the treatment of non-conservative products and an a posteriori stabilization procedure derived from the so-called Multidimensional Optimal Order Detection(MOOD)paradigm.In this work we consider the seven equation Baer-Nunziato model of compressible multi-phase flows as a representative model involving non-conservative products as well as relaxation source terms which are allowed to become stiff.The new scheme is validated against a set of test cases on 2D/3D unstructured moving meshes on parallel machines and the high order of accuracy achieved by the method is demonstrated by performing a numerical convergence study.Classical Riemann problems and explosion problems with exact solutions are simulated in 2D and 3D.The overall numerical code is also profiled to provide an estimate of the computational cost required by each component of the whole algorithm.
