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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms

As of 21 August 2026, this Paper Citation Record lists 72 of 72 outbound references and 0 inbound Pith citation observations for arXiv:2509.26284.

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2509.26284 v3

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measured 72 of 72 reference resolution

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Outbound references

Observation 97f6ceb6-9845-4451-bd92-0df7ccb7db12 · outbound

This paper cites A high-order nonconservative ap- proach for hyperbolic equations in fluid dynamics.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A high-order nonconservative ap- proach for hyperbolic equations in fluid dynamics

Reference 1

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Observation 862b6deb-1f9c-4b03-93dc-0f7cf3748bc6 · outbound

This paper cites A comment on the computation of non-conservative products.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A comment on the computation of non-conservative products

Reference 2

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Observation a1fd3940-44ab-4e65-8bc2-b8f697a265a1 · outbound

This paper cites High order methods for CFD.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms High order methods for CFD

Reference 3

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Observation d24b2811-9147-470c-80ec-cb90eade6ea1 · outbound

This paper cites A five-equation model for the simulation of interfaces between compressible fluids.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A five-equation model for the simulation of interfaces between compressible fluids

Reference 4

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Observation e3ba172f-9f62-47cf-b76d-fa2b22f3f50b · outbound

This paper cites An efficient covariant frame for the spherical shallow water equations: well balanced DG approximation and application to tsunami and storm surge.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms An efficient covariant frame for the spherical shallow water equations: well balanced DG approximation and application to tsunami and storm surge

Reference 5

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Observation f6fcadc9-b01f-45a6-84be-f88c1e66fe42 · outbound

This paper cites High-order adaptive discontinuous finite elements for the shallow water equations with sub-grid irregular bathymetry.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms High-order adaptive discontinuous finite elements for the shallow water equations with sub-grid irregular bathymetry

Reference 6

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Observation aec90056-ee45-4f29-8316-20484ef01de6 · outbound

This paper cites A two-phase mixture theory for the deflagration- to-detonation transition (DDT) in reactive granular materials.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A two-phase mixture theory for the deflagration- to-detonation transition (DDT) in reactive granular materials

Reference 7

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Observation ebe3fab0-76e3-4015-bda6-85f8c5d5a943 · outbound

This paper cites A High-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A High-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations

Reference 8

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Observation 432c3316-d7d0-4838-9116-579a57f80937 · outbound

This paper cites Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Multidimensional fully adaptive lattice Boltzmann methods with error control based on multiresolution analysis

Reference 9

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Observation f0a11d74-2789-41d3-bbb1-98352f733df7 · outbound

This paper cites Vanishing viscosity solutions of nonlinear hyper- bolic systems.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Vanishing viscosity solutions of nonlinear hyper- bolic systems

Reference 10

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Observation a34cb46a-828b-4a4d-a089-5c732efdb6be · outbound

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Unresolved cited work

Reference 11

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Observation 81aea716-9524-4f7a-b568-6165935c6bbb · outbound

This paper cites An entropy satisfying scheme for two-layer shal- low water equations with uncoupled treatment.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms An entropy satisfying scheme for two-layer shal- low water equations with uncoupled treatment

Reference 12

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Observation c2a924fc-2a86-4534-9770-00154d697755 · outbound

This paper cites On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms On thermodynamically compatible finite volume methods and path-conservative ADER discontinuous Galerkin schemes for turbulent shallow water flows

Reference 13

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Observation 1ed281b9-ddea-477a-9b8a-2df98f32373e · outbound

This paper cites High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms High order finite volume schemes based on reconstruction of states for solving hyperbolic systems with nonconservative products. Applications to shallow-water systems

Reference 14

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Observation 5a283822-f4ad-4c3b-8fe6-3f5cb30e0652 · outbound

This paper cites Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Why many theories of shock waves are necessary: Convergence error in formally path-consistent schemes

Reference 15

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Observation 8959f6ba-5d19-4d07-a49f-efa3a4327e86 · outbound

This paper cites High order extensions of Roe schemes for two-dimensional nonconservative hyperbolic systems.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms High order extensions of Roe schemes for two-dimensional nonconservative hyperbolic systems

Reference 16

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Observation 6fcbd032-c904-47ca-aaf3-7be06b02ad19 · outbound

This paper cites A new comment on the computation of non-conservative products using Roe-type path conservative schemes.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A new comment on the computation of non-conservative products using Roe-type path conservative schemes

Reference 17

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Observation 518b434e-fc5c-4370-afe8-355fd9158bd4 · outbound

This paper cites A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A positive and entropy-satisfying finite volume scheme for the Baer-Nunziato model

Reference 18

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Observation c2646c93-d7a9-4f68-aa05-6271458f9a2c · outbound

This paper cites Approximate solutions of the Baer-Nunziato model.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Approximate solutions of the Baer-Nunziato model

Reference 19

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Observation ec725da8-15ee-4bc0-a40b-b684f4af827c · outbound

This paper cites Definition and weak stability of nonconservative products.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Definition and weak stability of nonconservative products

Reference 20

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Observation aef65289-2ed8-4091-b726-79bead3d2fa2 · outbound

This paper cites Simplified Second-Order Godunov-Type Methods.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Simplified Second-Order Godunov-Type Methods

Reference 21

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Observation 07e8d917-a4ef-49ee-8ea0-e47ee8e41032 · outbound

This paper cites HLLC-type and path-conservative schemes for a single-velocity six-equation two-phase flow model: A comparative study.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms HLLC-type and path-conservative schemes for a single-velocity six-equation two-phase flow model: A comparative study

Reference 22

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Observation accc27f7-02cb-41ce-84d1-5c34800fd5f6 · outbound

This paper cites A new efficient formulation of the HLLEM Rie- mann solver for general conservative and non-conservative hyperbolic systems.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A new efficient formulation of the HLLEM Rie- mann solver for general conservative and non-conservative hyperbolic systems

Reference 23

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Observation 9d1537b0-3f54-4018-a02c-511b1fa70480 · outbound

This paper cites High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: applica- tions to compressible multi-phase flows.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms High-order unstructured Lagrangian one-step WENO finite volume schemes for non-conservative hyperbolic systems: applica- tions to compressible multi-phase flows

Reference 24

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Observation 0b881653-4f5f-472b-a11d-27df3d45b940 · outbound

This paper cites A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A simple extension of the Osher Riemann solver to non-conservative hyperbolic systems

Reference 25

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Observation e2362668-e428-4cb9-a078-13f71e7eed26 · outbound

This paper cites ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms ADER schemes on unstructured meshes for nonconservative hyperbolic systems: Applications to geophysical flows

Reference 26

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Observation c8a8af59-1a0a-4811-8584-97a01dcbc4ff · outbound

This paper cites FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms FORCE schemes on unstructured meshes II: Non-conservative hyperbolic systems

Reference 27

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Observation 9878b4e7-fddb-4885-a59a-4532e8c0d1b7 · outbound

This paper cites Upwind methods for the Baer-Nunziato equations and higher- order reconstruction using artificial viscosity.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Upwind methods for the Baer-Nunziato equations and higher- order reconstruction using artificial viscosity

Reference 28

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Observation 53b58555-5475-4a87-a8a5-c5d338aaae25 · outbound

This paper cites Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: quasi-conservative formulation with subcell finite vol- ume corrections.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Discontinuous Galerkin schemes for hyperbolic systems in non-conservative variables: quasi-conservative formulation with subcell finite vol- ume corrections

Reference 29

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Observation eba2a22d-3943-4b9e-a86c-624206154e5c · outbound

This paper cites Numerical modeling of two-phase flows using the two-fluid two-pressure approach.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Numerical modeling of two-phase flows using the two-fluid two-pressure approach

Reference 30

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Observation 9ef4a0b3-0df4-4f1d-9875-551d9c125869 · outbound

This paper cites A scalable well-balanced numerical scheme for the modeling of two-phase shallow granular landslide consolidation.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A scalable well-balanced numerical scheme for the modeling of two-phase shallow granular landslide consolidation

Reference 31

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This paper cites An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms An arbitrary high order well-balanced ADER-DG numerical scheme for the multilayer shallow-water model with variable density

Reference 32

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This paper cites Numerical methods and relaxation techniques for diffuse interface models in high-velocity two-phase flow simulations.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Numerical methods and relaxation techniques for diffuse interface models in high-velocity two-phase flow simulations

Reference 33

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Observation 8b253d1c-9838-45b5-91d2-c45e190e18f9 · outbound

This paper cites Haegeman et al.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Haegeman et al

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Observation a266c09a-bb91-469b-8699-b43003326a15 · outbound

This paper cites Multiresolution Algorithms for the Numerical Solution of Hyperbolic Conservation Laws.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Multiresolution Algorithms for the Numerical Solution of Hyperbolic Conservation Laws

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Two approaches to compute unsteady compress- ible two-phase flow models with stiff relaxation terms

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Why nonconservative schemes converge to wrong solutions: error analysis

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Two-phase modeling of deflagration-to-detonation transition in granular materials: Reduced equations

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Ketcheson, R.J

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms High-order wave propagation algorithms for hyperbolic systems

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms The Noble-Abel Stiffened-Gas equation of state

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Unresolved cited work

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Observation 28c56817-a682-40ab-9df1-b3fd784b1a6e · outbound

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms HLLC-type Riemann solver with approximated two-phase con- tact for the computation of the Baer-Nunziato two-fluid model

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A five equation reduced model for compressible two phase flow problems

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A path-conservative finite volume scheme for compressible multi-phase flows with surface tension

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Modelling and simulations of two-phase flows including geometric variables

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A comparative Fourier analysis of discontinuous Galerkin schemes for advection-diffusion with respect to BR1, BR2, and local discontinuous Galerkin diffusion discretization

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Numerical methods for nonconservative hyperbolic systems: a theo- retical framework

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Wave structure similarity of the HLLC and Roe Riemann solvers: Application to low Mach number preconditioning

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Arbitrary-rate relaxation techniques for the numerical modeling of compressible two-phase flows with heat and mass transfer

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A mixture-energy-consistent six-equation two- phase numerical model for fluids with interfaces, cavitation and evaporation waves

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A relaxation-projection method for compressible flows. Part II: Artificial heat exchanges for multiphase shocks

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This paper cites A pressure-based method for weakly compressible two- phase flows under a Baer-Nunziato type model with generic equations of state and pressure and velocity disequilibrium.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A pressure-based method for weakly compressible two- phase flows under a Baer-Nunziato type model with generic equations of state and pressure and velocity disequilibrium

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equa- tions

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms An accurate and efficient semi-implicit method for section- averaged free-surface flow modelling

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms The calculation of the interaction of non-stationary shock waves and obstacles

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A relaxation scheme for a hyperbolic multiphase flow model - Part I: Barotropic EOS

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A Multiphase Godunov Method for Compressible Multifluid and Multiphase Flows

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Modelling phase transition in metastable liquids: application to cavitating and flashing flows

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Observation e0f5024a-68a9-4819-822f-e319c2f870b3 · outbound

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Simple and efficient relaxation meth- ods for interfaces separating compressible fluids, cavitating flows and shocks in multiphase mixtures

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Observation 411e4046-cfcc-4f8f-8e3c-d6dc788bd1c2 · outbound

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Shock Jump Relations for Multiphase Mixtures with Stiff Me- chanical Relaxation

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Modelling interactions between waves and diffused in- terfaces

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms The Riemann problem and a high-resolution Godunov method for a model of compressible two-phase flow

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Mixture-conservative temperature-based Baer-Nunziato solver for efficient full-disequilibrium simulations of real fluids

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Observation 65fbc167-a787-4533-a215-d8f38b0fae7e · outbound

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms An explicit primitive conservative solver for the Euler equations with arbitrary equation of state

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Observation 4334f648-37e2-4e40-9163-bc3cba1ce1a1 · outbound

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms HLLC-type Riemann solver for the Baer-Nunziato equations of compressible two-phase flow

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Unresolved cited work

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Observation 6d9e8db7-79ee-4453-a9c4-f74e2aa69ce2 · outbound

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A semi-implicit, semi-Lagrangian discontinu- ous Galerkin framework for adaptive numerical weather prediction

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms A limiter-based well-balanced discontin- uous Galerkin method for shallow-water flows with wetting and drying: Trian- gular grids

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This paper cites Numerical Treatment of the Nonconservative Product in a Multiscale Fluid Model for Plasmas in Thermal Nonequilibrium: Application to Solar Physics.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Numerical Treatment of the Nonconservative Product in a Multiscale Fluid Model for Plasmas in Thermal Nonequilibrium: Application to Solar Physics

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A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Unresolved cited work

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This paper cites Modeling phase transition for compress- ible two-phase flows applied to metastable liquids.

A robust computational framework for the mixture-energy-consistent six-equation two-phase model with instantaneous mechanical relaxation terms Modeling phase transition for compress- ible two-phase flows applied to metastable liquids

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