Evgeniy Romenski

Russian Academy of Sciences | RAS · Sobolev Institute of Mathematics

We present a unified nonequilibrium model of continuum mechanics for compressible multiphase flows. The model, which is formulated within the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) equations, can describe the arbitrary number of phases that can be heat-conducting inviscid and viscous fluids, as well as elastoplastic s...

How to properly describe continuum thermodynamics of binary mixtures where each constituent has its own momentum? The Symmetric Hyperbolic Thermodynamically Consistent (SHTC) framework and Hamiltonian mechanics in the form of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provide two answers, which are similar b...

In continuum thermodynamics, models of two-phase mixtures typically obey the condition of pressure equilibrium across interfaces between the phases. We propose a new non-equilibrium model beyond that condition, allowing for microinertia of the interfaces, surface tension, and different phase pressures. The model is formulated within the framework o...

A computational model is presented for simulations small amplitude wavefields in a deformable porous medium saturated with a compressible fluid under temperature variations. The model is based on the governing equations derived with the use of the theory of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems in conjunction with the eff...

A two-phase flow model for compressible immiscible fluids is presented, the derivation of which is based on the use of the theory of symmetric hyperbolic thermodynamically compatible systems. The model is an extension of the previously proposed thermodynamically compatible model of compressible two-phase flows due to the inclusion of new state vari...

In this paper we present a new family of semi-discrete and fully-discrete finite volume schemes for overdetermined, hyperbolic and thermodynamically compatible PDE systems. In the following we will denote these methods as HTC schemes. In particular, we consider the Euler equations of compressible gasdynamics, as well as the more complex Godunov-Pes...

Motivated by numerically solving the Einstein field equations, we derive a first-order reduction of the second-order $ f(T) $-teleparallel gravity field equations in the pure-tetrad formulation (no spin connection). We then restrict our attention to the teleparallel equivalent of general relativity (TEGR) and propose a 3+1 decomposition of the gove...

In this work we study the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model introduced in Romenski et al. (J Sci Comput 42(1):68, 2009, Quart Appl Math 65(2):259–279, 2007). All characteristic fields are carefully studied and explicit expr...

In this paper we present a new family of semi-discrete and fully-discrete finite volume schemes for overdetermined, hyperbolic and thermodynamically compatible PDE systems. In the following we will denote these methods as HTC schemes. In particular, we consider the Euler equations of compressible gasdynamics, as well as the more complex Godunov-Pe...

In this work we study the solution of the Riemann problem for the barotropic version of the conservative symmetric hyperbolic and thermodynamically compatible (SHTC) two-phase flow model introduced in \cite{Romenski2007,Romenski2009}. All characteristic fields are carefully studied and explicit expressions are derived for the Riemann invariants and...

A new hyperbolic two-phase model of a porous deformable medium saturated with a viscous fluid is presented and some of its features or performances are discussed. The governing equations are derived in the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems. The model accounts for such dissipative mechanisms as interfacial...

How to properly describe continuum thermodynamics of binary mixtures where each constituent has its own momentum? The Symmetric Hyperbolic Thermodynamically Consistent (SHTC) framework and Hamiltonian mechanics in the form of the General Equation for Non-Equilibrium Reversible-Irreversible Coupling (GENERIC) provide two answers, which are similar b...

A computational model of interaction of a compressible fluid and deformable elastic solid is presented. The model is derived from the general solid-fluid two-phase mixture model and its derivation is based on the Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems theory. The governing equations form a symmetric hyperbolic system of pa...

A new model of compressible multiphase flow in a deforming porous medium under finite deformations is presented. The derivation of the model is based on the application of the theory of a Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems to a multiphase mixture of solid and fluids. The viscosity of the saturating fluid can be taken i...

A new three-phase model of compressible two-fluid flows in a deformed porous medium is presented. The derivation of the model is based on the application of the Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems theory to three-phase solid-fluid mixture. The resulting governing equations are hyperbolic and satisfy the laws of irrevers...

We present a model and numerical technique method for simulation a small-amplitude wave propagation in the fluid-saturated porous medium in regions with different porosity, including domains with pure fluid and pure solid. The governing equations are derived from the general hyperbolic thermodynamically compatible model of compressible fluid flow i...

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids, also called yield-stress fluids. In contrast to the conventional approaches relying on the non-linear viscosit...

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealized infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones, here we present a first-order hyperbolic and thermodynamically com...

We derive and study a new hyperbolic two-phase model of a porous deformable medium saturated by a viscous fluid. The governing equations of the model are derived in the framework of Symmetric Hyperbolic Thermodynamically Compatible (SHTC) systems and by generalizing the unified hyperbolic model of continuum fluid and solid mechanics. Similarly to t...

We propose a new pressure-based structure-preserving (SP) and quasi asymptotic preserving (AP) staggered semi-implicit finite volume scheme for the unified first order hyperbolic formulation of continuum mechanics [1], which goes back to the pioneering work of Godunov [2] and further work of Godunov & Romenski [3] and Peshkov & Romenski [4]. The un...

We discuss the applicability of a unified hyperbolic model for continuum fluid and solid mechanics to modeling non-Newtonian flows and in particular to modeling the stress-driven solid-fluid transformations in flows of viscoplastic fluids, also called yield-stress fluids. In contrast to the conventional approaches relying on the non-linear viscosit...

A computational model for the small amplitude wave propagation in an elastic porous medium saturated by the viscous compressible fluid is discussed. The presented model is an extension of the model [1] and its derivation is based on the symmetric hyperbolic thermodynamically compatible system for two-phase solid-fluid mixture with finite deformatio...

We are concerned with the numerical solution of a unified first order hyperbolic formulation of continuum mechanics that goes back to the work of Godunov, Peshkov and Romenski [64], [67], [96] (GPR model) and which is an extension of nonlinear hyperelasticity that is able to describe simultaneously nonlinear elasto-plastic solids at large strain, a...

Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities and multi-physics coupling within and outside of fault zones, here we present a first order hyperbolic and thermodynamically com...

We propose a new pressure-based structure-preserving (SP) and quasi asymptotic preserving (AP) staggered semi-implicit finite volume scheme for the unified first order hyperbolic formulation of continuum mechanics. The unified model is based on the theory of symmetric-hyperbolic and thermodynamically compatible (SHTC) systems and includes the descr...

A multiphase model and its application to wavefields numerical simulation are discussed in the context of modeling of compressible fluid flows in elastic porous media. The derivation of the model is based on a theory of thermodynamically compatible systems and on a model of nonlinear elastoplasticity combined with a multiphase compressible fluid fl...

The new two-phase model for compressible fluid flows in nonlinear poroelastoplastic media is presented. The derivation of the model is based on the symmetric hyperbolic thermodynamically compatible systems theory, which is developed with the use of the first principles and fundamental laws of irreversible thermodynamics. The governing PDEs form the...

The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein’s special relativity and the Euler–Lagrange structure of general relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC...

We are concerned with the numerical solution of a unified first order hyperbolic formulation of continuum mechanics that originates from the work of Godunov, Peshkov and Romenski (GPR model) and which is an extension of nonlinear hyperelasticity that is able to describe simultaneously nonlinear elasto-plastic solids at large strain, as well as visc...

This book is a liber amicorum to Professor Sergei Konstantinovich Godunov and gathers contributions by renowned scientists in honor of his 90th birthday. The contributions address those fields that Professor Godunov is most famous for: differential and difference equations, partial differential equations, equations of mathematical physics, mathemat...

A multiphase model and its application to wavefields numerical simulation are discussed in the context of modeling of compressible fluid flows in elastic porous media. The derivation of the model is based on a theory of thermodynamically compatible systems and on a model of nonlinear elastoplasticity combined with a multiphase compressible fluid fl...

The lack of formulation of macroscopic equations for irreversible dynamics of viscous heat-conducting media compatible with the causality principle of Einstein's Special Relativity and the Euler-Lagrange structure of General Relativity is a long-lasting problem. In this paper, we propose a possible solution to this problem in the framework of SHTC...

We present a unified causal general relativistic formulation of dissipative and non-dissipative continuum mechanics. The presented theory is the first general relativistic theory that can deal simultaneously with viscous fluids as well as irreversible deformations in solids and hence it also provides a fully covariant formulation of the Newtonian c...

This paper is an attempt to introduce methods and concepts of the Riemann–Cartan geometry largely used in such physical theories as general relativity, gauge theories, solid dynamics to fluid dynamics in general and to studying and modeling turbulence in particular. Thus, in order to account for the rotational degrees of freedom of the irregular dy...

The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discus...

Continuum mechanics with dislocations, with the Cattaneo type heat conduction, with mass transfer, and with electromagnetic fields is put into the Hamiltonian form and into the form of the Godunov type system of the first order, symmetric hyperbolic partial differential equations (SHTC equations). The compatibility with thermodynamics of the time r...

This paper is an attempt to introduce methods and concepts of the Riemann-Cartan geometry largely used in such physical theories as general relativity, gauge theories, solid dynamics, etc. to fluid dynamics in general and to studying and modeling turbulence in particular. Thus, in order to account for the rotational degrees of freedom of the irr...

In this paper we propose a new flux splitting approach for the symmetric hyperbolic thermodynamically compatible (SHTC) equations of compressible two-phase flow which can be used in finite-volume methods. The approach is based on splitting the entire model into acoustic and pseudo-convective submodels. The associated acoustic system is numerically...

In this paper we introduce a reformulation of the compressible multicomponent Navier-Stokes equations that govern the behaviour of mixtures of miscible gases. The resulting equation set is a first-order hyperbolic system containing stiff source terms, which recovers the conventional parabolic theory of viscosity, conduction and diffusion as a first...

A General Relativistic formulation of continuum mechanics is discused. This includes viscous fluids, elastic and inelastic solids. The governing equations are hyperbolic and admit only finite speeds for perturbation propagation (causality). Due to their Hamiltonian nature, the equations are compatible with the Einstein field equations of gravity. S...

We discuss a unified flow theory which in a single system of hyperbolic partial differential equations (PDEs) can describe the two main branches of continuum mechanics, fluid dynamics, and solid dynamics. The fundamental difference from the classical continuum models, such as the Navier-Stokes for example, is that the finite length scale of the con...

The aim of this paper is to compare a hyperelastic with a hypoelastic model describing the Eulerian dynamics of solids in the context of non-linear elastoplastic deformations. Specifically, we consider the well-known hypoelastic Wilkins model, which is compared against a hyperelastic model based on the work of Godunov and Romenski. First, we discus...

Based on the theory of thermodynamically compatible systems, we formulate the governing equations of a gas-liquid compressible pipe flow and develop the Runge–Kutta–TVD and Runge–Kutta–WENO high accuracy methods. The computational model is used to solve a series of test cases demonstrating its efficiency and capability to be applied to slug flows m...

A numerical technique for solving an initial-boundary value problem of the single compressible fluid flow through elastic porous medium is presented. The model of compressible fluid flow in elastic porous medium is derived within the theory of hyperbolic thermodynamically compatible systems of conservation laws that provides a formulation of mathem...

The constitutive equations of motion of an elastic medium with given initial stresses are formulated in the form of a hyperbolic system of first order differential equations. Equations describing the propagation of small perturbations in a prestressed isotropic medium with an arbitrary dependence of the elastic strain energy on the strain tensor ar...

The paper considers failure of a stratum within the framework of a nonlocal elasticity theory for a plastic flow. Here, the nonlocality is determined by dependence between deformation energy and metric deformation tensor derivatives. Our study has demonstrated that in case of a stratum under lateral stress, the spatial distribution of shear stress...

This work proposes the nonlinear model for the flow of mixture of compressible liquids in a porous medium with consideration of finite deformations and thermal effects. Development of this model is based on the method of thermodynamically consistent systems of conservation laws. Numerical analysis of the model is based on the WENO-Runge-Kutta metho...

In this paper, we propose a new unified first order hyperbolic model of Newtonian continuum mechanics coupled with electro-dynamics. The model is able to describe the behavior of moving elasto-plastic dielectric solids as well as viscous and inviscid fluids in the presence of electro-magnetic fields. It is actually a very peculiar feature of the pr...

Measurement of permeability in borehole in the presence of mudcake

The two-phase two-pressure model for transient one-dimensional compressible pipe flow is considered. Governing equations of the model form a hyperbolic system of conservation laws. The Runge-Kutta-WENO method providing accuracy of the 3rd order in time and 5th order in space is implemented. Numerical results for several test problems are presented.

This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov & Romenski, denoted as HPR model. In that framework, the viscous stresses are computed from the so-called distortion tensor A, which is one of the primary state variables. A very important key fea...

Nonstationary theory of two-velocity continuum describing the propagation of acoustic waves inmicrofractured porousmedia is based on general physical principles: the first law of thermodynamics, the conservation laws, the kinematic relationships in the metric tensor and the Galilean principle of relativity. As a physical application, the theory of...

A method for estimating the stress–strain state of a rock massif in the vicinity of underground facilities is substantiated. This method is based on solution of the boundary inverse problem of defining the components of an external stress field from the acoustic sounding data. The acoustic sounding data used are the arrival times of diving head lon...

This is a talk given on several seminars: LJLL (Paris, 27/11/2015), LMFA (Lyon, 20/11/2015), IMFT (Toulouse, 26/11/2015), IPRA (Pau, 12/11/2015). The presentation contains a popular explanation of the unified continuum model recently proposed in http://arxiv.org/abs/1403.8068 and http://arxiv.org/abs/1511.08995. The model can describe in one single...

A spatially non-local model for inelastic deformation of solids is proposed and studied. The non-locality of deformation is taken into account by the additional parameter of state beyond the classical parameters such as stress and strain tensors. This additional parameter is the curvature tensor expressed in terms of the metric strain tensor, and i...

A talk given on the 7th International Workshop on Nonequilibrium Thermodynamics (IWNET). We discuss a unified framework for modeling of flows of viscous fluids and dynamics of solids. The mathematical model is formulated as a first order system of PDEs of hyperbolic type. Its relation to GENERIC approach as well as the Extended Irreversible Thermod...

Abstract Rock behaviour frequently does not fit the classical theory of continuum mechanics because of rock aggregated granular structure. Particularly, rock fracturing may be accompanied by zonal disintegration formation. The key to building the non-classic model of rock fracturing is the granulated structure. Deformations of solid bodies with mic...

The new computational model for the seismic wave propagation is proposed, the governing equations of which are written in terms of velocities, stress tensor and small rotation of element of the medium. The properties of wavefields in the prestressed medium are studied and some examples showing anisotropy of prestressed state are discussed. The stag...

An application of the theory of thermodynamically compatible hyperbolic systems to design a multiphase compressible flow models is discussed. With the use of such approach the governing equations are derived from the first principles, formulated in a divergent form and can be transformed to a symmetric hyperbolic system in the sense of Friedrichs....

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A model for multidimensional compressible two-phase flow with pressure and velocity relaxations based on the theory of thermodynamically compatible system is extended to study liquid-€“gas flows with cavitation. The model assumes for each phase its own pressure and velocity, while a common temperature is considered. The governing equations form a h...

A high-accuracy Runge-Kutta/WENO method of up to fourth order with respect to time and fifth order with respect to space is developed for the numerical modeling of small-amplitude wave propagation in a steady fluid-saturated elastic porous medium. A system of governing equations is derived from a general thermodynamically consistent model of a comp...

Derivation of governing equations for multiphase flow on the base of thermodynamically compatible systems theory is presented. The mixture is considered as a continuum in which the multiphase character of the flow is taken into account. The resulting governing equations of the formulated model belong to the class of hyperbolic systems of conservati...

We discuss a pure hyperbolic alternative to the Navier-Stokes equations, which are of parabolic type. As a result of the substitution of the concept of the viscosity coefficient by a microphysics-based temporal characteristic, particle settled life (PSL) time, it becomes possible to formulate a model for viscous fluids in a form of first order hype...

On the example of two-phase continua experiencing stress-induced solid–fluid phase transitions, we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the time evolution equations possessing it are compatible with mechanics and with thermodynamics. The former compati...

The conservative hyperbolic formulation for compressible multiphase flow for the case of four phase flow is presented. The properties of governing equations are described and numerical results for some Riemann test problems are shown.

A basis for the development of numerical framework to modelling seismic wave propagation through prestressed zones is proposed. The governing equations for elastic waves in prestressed media written in stress-velocity formulation supplemented by the small rotation tensor equation are presented. The simplified version of equations is considered, ass...

On the example of two-phase continua experiencing stress induced solid-fluid phase transitions we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the time evolution equations possessing it are compatible with mechanics and with thermodynamics. The former compatib...

A model for compressible two-phase flow with pressure and velocity relaxations and phase transition is presented. The model assumes for each phase its own pressure and velocity, while a common temperature is considered. The governing equations form an hyperbolic system in conservative form and are derived through the theory of thermodynamically com...

The interest in Stoneley waves in wellbores drilled through porous media comes from the dependence of its attenuation on formation permeability. This property makes the Stoneley waves an important tool for measuring the permeability of the porous medium [Xianyun, Hezhu, 2007; Dorovsky V. et al. 2010]. Drilling technology induces mudcake buildup bet...

In this work, we present results on mathematical modelling of polymeric yield stress fluids which have the properties of both elastic solids and fluids. Our research is based on the approach of multiphase continuum mechanics. A two-phase solid-fluid model is developed. This model is thermodynamically compatible and its governing differential equati...

Derivation of governing equations for multiphase flow on the basis of thermodynamically compatible systems theory is presented. The application of the theory to conservative formulations of compressible multiphase flow with arbitrary number of phases is proposed and governing equations for the single temperature multiphase flow are formulated and d...

A mudcake formed on the borehole wall between a fluid-filled porous formation and the borehole fluid can affect Stoneley wave propagation used to estimate the formation permeability. The mudcake effect on the permeability dependence of radial oscillations of borehole fluid is investigated in a system with a source generating radial acoustic waves i...

In this paper we show that entropy can be used within a functional for the stress relaxation time of solid materials to parametrise finite viscoplastic strain-hardening deformations. Through doing so the classical empirical recovery of a suit-able irreversible scalar measure of work-hardening from the three-dimensional state parameters is avoided....

A conservative hyperbolic model for compressible two-phase two-uid model is studied and numerical methods for its approximate solution are proposed. The derivation of the governing equations of the model is based on the principles of extended thermodynamics. The eld equations form a hyperbolic system of balance equations in conservative form, which...

A physically simple method is suggested to measure the permeability of porous reservoirs on the basis of resonance radial oscillations of borehole fluid. The interfacial velocity difference between the porous solid and the fluid is highly sensitive to the permeability of the formation outside the borehole at the resonance frequency. Thus, the perme...

We present a continual model of an elastic medium with a field of distributed defects and use it to study the frequency transformation effect in elastic waves. By an example of simulation of the one-dimensional waves arising under a harmonic action on a layer with defects, we demonstrate the possibility of describing frequency transformation in the...

The paper presents the computational framework for solving hyperbolic models for compressible two-phase flow by finite volume methods. A hierarchy of two-phase flow systems of conservation-form equations is formulated, including a general model with different phase velocities, pressures and temperatures; a simplified single temperature model with...

Eulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to non-linear elastic theory. In this paper one such class of solver is examined based up...

Conservative formulations of the governing laws of elastoplastic solid media have distinct advantages when solved using high-order shock capturing methods for simulating processes involving large deformations and shock waves. In this paper one such model is considered where inelastic deformations are accounted for via conservation laws for elastic...

The present work is devoted to the computational modelling of the process of beam action on a lithium target. The aim of the investigation is to determine the maximum values of temperature and pressure as well as general pattern of the process. The analysis is based on the compressible Euler equations with the stiffened gas equation of state with p...

This paper outlines the development of a two-phase flow model based on the theory of thermodynamically compatible systems of hyperbolic conservation laws. The conservative hyperbolic governing equations are numerically implemented in conjunction with the second-order MUSCL method and the GFORCE flux, while for the reduced isentropic model the first...

The present paper is devoted to the construction and comparative study of upwind methods as applied to the system of one-dimensional non-linear elasticity equations with particular attention to robustness and accurate resolution of delicate features such as linearly degenerate fields. Copyright © 2007 John Wiley & Sons, Ltd.

Full-text of this article is not available in this e-prints service. This article was originally published [following peer-review] in International Journal for Numerical Methods in Fluids, published by and copyright John Wiley & Sons. We propose a new model and a solution method for two-phase two-fluid compressible flows. The model involves six equ...

Constitutive equations that describe the experimentally observed failure waves are proposed to model inelastic strains of brittle materials. The complete system of equations is hyperbolic, each equation of this system has divergent form. The model is based on the assumption that continual failure is the process of transition from an intact state to...