James Glimm - Academia.edu (original) (raw)

Papers by James Glimm

Research paper thumbnail of Global Solutions to the Compressible Euler Equations with Geometrical Structure

We prove the existence of global solutions to the Euler equations of compressible isentropicgas d... more We prove the existence of global solutions to the Euler equations of compressible isentropicgas dynamics with geometrical structure, including transonic nozzle flow and spherically symmetric flow.Due to the presence of the geometrical source terms, the existence results themselves are new, especiallyas they pertain to radial flow in an unbounded region, j~xj 1, and to transonic nozzle flow. Arbitrarydata with L1bounds

Research paper thumbnail of The bifurcation of tracked scalar waves

Siam Journal on Scientific and Statistical Computing, 1988

The dynamic evolution of tracked waves by a front-tracking algorithm may lead on either numerical... more The dynamic evolution of tracked waves by a front-tracking algorithm may lead on either numerical or physical grounds to intersections. The correct resolution of these intersections is described locally by the solution of Riemann problems and requires a bifurcation of the topology defined by the tracked waves. Here the authors describe an algorithm that is appropriate for the resolution of

Research paper thumbnail of The dynamics of bubble growth for Rayleigh–Taylor unstable interfaces

Physics of Fluids, 1988

A statistical model is analyzed for the growth of bubbles in a Rayleigh–Taylor unstable interface... more A statistical model is analyzed for the growth of bubbles in a Rayleigh–Taylor unstable interface. The model is compared to solutions of the full Euler equations for compressible two phase flow, using numerical solutions based on the method of front tracking. The front tracking method has the distinguishing feature of being a predominantly Eulerian method in which sharp interfaces are

Research paper thumbnail of A QMU approach for characterizing the operability limits of air-breathing hypersonic vehicles

Reliability Engineering & System Safety, 2011

The operability limits of a supersonic combustion engine for an air-breathing hypersonic vehicle ... more The operability limits of a supersonic combustion engine for an air-breathing hypersonic vehicle are characterized using numerical simulations and an uncertainty quantification methodology. The time-dependent compressible flow equations with heat release are solved in a simplified configuration. Verification, calibration and validation are carried out to assess the ability of the model to reproduce the flow/thermal interactions that occur when the engine unstarts due to thermal choking. Quantification of Margins and Uncertainty (QMU) is used to determine the safe operation region for a range of fuel flow rates and combustor geometries.

Research paper thumbnail of A two-phase flow model of the Rayleigh-Taylor mixing zone

Physics of Fluids, 1996

The Rayleigh-Taylor instability of an interface separating fluids of distinct density is drivenby... more The Rayleigh-Taylor instability of an interface separating fluids of distinct density is drivenby an acceleration across the interface. Low order statistical moments of fluctuating fluidquantities characterize the hydrodynamics of the mixing zone.A new model is proposed for the momentum coupling between the two phases. Thismodel is validated against computational data for compressible flows, including flows near theincompressible limit. Our main

Research paper thumbnail of An Embedded Boundary Method for Solving the Elliptic And Parabolic Interface Problems and Its application to the Stefan Problem

The embedded boundary method (EBM) on a Cartesian grid developed by Johansen and Colella has been... more The embedded boundary method (EBM) on a Cartesian grid developed by Johansen and Colella has been extended to solve the elliptic/parabolic problems in 2D with an interior boundary (also called elliptic interface, parabolic interface problem). The method is a finite volume method. 2nd order accuracy in L∞ norm is achieved. As its application, a Stefan problem is solved. Problems with

Research paper thumbnail of Numerical Simulations of Free Surface Magnetohydrodynamic Flows

We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) fr... more We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) free surface flows. The corresponding system of MHD equations is a system of strongly coupled hyperbolic and parabolic/elliptic equations in moving and geometrically complex domains. The hyperbolic system is solved using the front tracking technique for the free fluid interface. Parallel algorithms for solving elliptic and parabolic equations

Research paper thumbnail of A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

Journal of Computational Physics, 2007

We have developed a numerical algorithm and computational software for the study of magnetohydrod... more We have developed a numerical algorithm and computational software for the study of magnetohydrodynamics (MHD) of free surface flows at low magnetic Reynolds numbers. The governing system of equations is a coupled hyperbolic–elliptic system in moving and geometrically complex domains. The numerical algorithm employs the method of front tracking and the Riemann problem for material interfaces, second order Godunov-type hyperbolic

Research paper thumbnail of Dynamic Phase Boundaries for Compressible Fluids

Siam Journal on Scientific Computing, 2008

We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. W... more We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. We model the transition as a tracked jump discontinuity. The emphasis here is on the coupling of the phase transition process to acoustic waves, which is required for the study of cavitation induced by strong rarefaction waves. The robustness of the proposed algorithm is verified by application to various physical regimes.

Research paper thumbnail of Direct Numerical Simulation of Bubbly Flows and Application to Cavitation Mitigation

Journal of Fluids Engineering-transactions of The Asme, 2007

The direct numerical simulation (DNS) method has been used to the study of the linear and shock w... more The direct numerical simulation (DNS) method has been used to the study of the linear and shock wave propagation in bubbly fluids and the estimation of the efficiency of the cavitation mitigation in the container of the Spallation Neutron Source liquid mercury target. The DNS method for bubbly flows is based on the front tracking technique developed for free surface flows. Our front tracking hydrodynamic simulation code FronTier is capable of tracking and resolving topological changes of a large number of interfaces in two-and three-dimensional spaces. Both the bubbles and the fluid are compressible. In the application to the cavitation mitigation by bubble injection in the SNS, the collapse pressure of cavitation bubbles was calculated by solving the Keller equation with the liquid pressure obtained from the DNS of the bubbly flows. Simulations of the propagation of linear and shock waves in bubbly fluids have been performed, and a good agreement with theoretical predictions and experiments has been achieved. The validated DNS method for bubbly flows has been applied to the cavitation mitigation estimation in the SNS. The pressure wave propagation in the pure and the bubbly mercury has been simulated, and the collapse pressure of cavitation bubbles has been calculated. The efficiency of the cavitation mitigation by bubble injection has been estimated. The DNS method for bubbly flows has been validated through comparison of simulations with theory and experiments. The use of layers of nondissolvable gas bubbles as a pressure mitigation technique to reduce the cavitation erosion has been confirmed.

Research paper thumbnail of A TSTT integrated FronTier code and its applications in computational fluid physics

Journal of Physics: Conference Series, 2005

We introduce the FronTier-Lite software package and its adaptation to the TSTT geometry and mesh ... more We introduce the FronTier-Lite software package and its adaptation to the TSTT geometry and mesh entity data interface. This package is extracted from the original front tracking code for general purpose scientific and engineering applications. The package contains a static interface library and a dynamic front propagation library. It can be used in research of different scientific problems. We demonstrate

Research paper thumbnail of A renormalization group scaling analysis for compressible two-phase flow

Physics of Fluids A: Fluid Dynamics, 1993

Computational solutions to the Rayleigh–Taylor fluid mixing problem, as modeled by the two‐fluid ... more Computational solutions to the Rayleigh–Taylor fluid mixing problem, as modeled by the two‐fluid two‐dimensional Euler equations, are presented. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a ...

Research paper thumbnail of From Cardiac Cells to Genetic Regulatory Networks

Lecture Notes in Computer Science, 2011

One of the fundamental questions in the treatment of ventricular cardiac disorders, such as tachy... more One of the fundamental questions in the treatment of ventricular cardiac disorders, such as tachycardia and fibrillation, is under what circumstances does such a disorder arise? To answer to this question, we develop a multiaffine hybrid automaton (MHA) cardiac-cell model, and restate the original question as one of identification of the parameter ranges under which the MHA model accurately reproduces the disorder. The MHA model is obtained from the minimal cardiac model of one of the authors (Fenton) by first bringing it into the form of a canonical, genetic regulatory network, and then linearizing its sigmoidal switches, in an optimal and global way. By leveraging the Rovergene tool for genetic regulatory networks, we are then able to successfully identify parameter ranges of interest.

Research paper thumbnail of Time dependent anomalous diffusion for flow in multi-fractal porous media

Lecture Notes in Physics, 1992

Macroscopic flow computations are used in the modelilig of most practical porous media flow studi... more Macroscopic flow computations are used in the modelilig of most practical porous media flow studies. These computations require macroscopic or effective flow parameters, describing effective fluid behavior over an integrated range of shorter length scales. This requirement is the ...

Research paper thumbnail of Errors in numerical solutions of spherically symmetric shock physics problems

Contemporary Mathematics, 2005

We seek robust and understandable error models for shock physics simulations. The purpose of this... more We seek robust and understandable error models for shock physics simulations. The purpose of this paper is to explore complications introduced by spherical flow in the analysis of errors in the numerical solution of shock interaction problems. In contrast to the case of planar waves, the spherical waves are not constant in strength between interactions and the solution is not piecewise constant between waves. Nevertheless simple power laws predict the dependence of the solution on the radius. We find that the same power laws predict the evolution of the error, as the error, once formed, propagates according to the same laws as govern the solution structures (i.e. the waves) themselves. We analyze errors in composite wave interaction problems based on the analysis of single interactions and a multi-path scattering formula to combine the effects of errors propagating through the individual interactions.

Research paper thumbnail of Three-Dimensional Front Tracking

Siam Journal on Scientific Computing, 1998

Page 1. THREE-DIMENSIONAL FRONT TRACKING ∗ JAMES GLIMM† , JOHN W. GROVE† , XIAO LIN LI‡ , KEH-MIN... more Page 1. THREE-DIMENSIONAL FRONT TRACKING ∗ JAMES GLIMM† , JOHN W. GROVE† , XIAO LIN LI‡ , KEH-MING SHYUE§ , YANNI ZENG† , AND QIANG ZHANG† SIAM J. SCI. COMPUT. c 1998 Society for Industrial and Applied Mathematics Vol. 19, No. 3, pp. ...

Research paper thumbnail of PROGRAM-AT-A- GLANCE

Research paper thumbnail of A theory of macrodispersion for the scale-up problem

Transport in Porous Media, 1993

Dispersion is the result, observable on large length scales, of events which are random on small ... more Dispersion is the result, observable on large length scales, of events which are random on small length scales. When the length scale on which the randomness operates is not small, relative to the observations, then classical dispersion theory fails. The scale up problem refers to situations in which randomness occurs on all length scales, and for which classical dispersion theory necessarily fails. The purpose of this article is to present non-Fickian, theories of dispersion, which do not assume a scale separation between the randomness and the observed consequences, and which do not assume a single length scale.

Research paper thumbnail of Dynamic Phase Boundaries for Compressible Fluids

SIAM Journal on Scientific Computing, 2008

We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. W... more We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. We model the transition as a tracked jump discontinuity. The emphasis here is on the coupling of the phase transition process to acoustic waves, which is required for the study of cavitation induced by strong rarefaction waves. The robustness of the proposed algorithm is verified by application to various physical regimes.

Research paper thumbnail of Statistical Riemann Problems and a Composition Law for Errors in Numerical Solutions of Shock Physics Problems

SIAM Journal on Scientific Computing, 2004

We seek error models for shock physics simulations that are robust and understandable. The purpos... more We seek error models for shock physics simulations that are robust and understandable. The purpose of this paper is to formulate and validate a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones. We illustrate this idea in a simple context. This paper employs several simplifying assumptions (restriction to one spatial dimension, use of a simplified (gamma law) equation of state, and consideration of a single numerical method). In separate papers we will address the effect of these assumptions.

Research paper thumbnail of Global Solutions to the Compressible Euler Equations with Geometrical Structure

We prove the existence of global solutions to the Euler equations of compressible isentropicgas d... more We prove the existence of global solutions to the Euler equations of compressible isentropicgas dynamics with geometrical structure, including transonic nozzle flow and spherically symmetric flow.Due to the presence of the geometrical source terms, the existence results themselves are new, especiallyas they pertain to radial flow in an unbounded region, j~xj 1, and to transonic nozzle flow. Arbitrarydata with L1bounds

Research paper thumbnail of The bifurcation of tracked scalar waves

Siam Journal on Scientific and Statistical Computing, 1988

The dynamic evolution of tracked waves by a front-tracking algorithm may lead on either numerical... more The dynamic evolution of tracked waves by a front-tracking algorithm may lead on either numerical or physical grounds to intersections. The correct resolution of these intersections is described locally by the solution of Riemann problems and requires a bifurcation of the topology defined by the tracked waves. Here the authors describe an algorithm that is appropriate for the resolution of

Research paper thumbnail of The dynamics of bubble growth for Rayleigh–Taylor unstable interfaces

Physics of Fluids, 1988

A statistical model is analyzed for the growth of bubbles in a Rayleigh–Taylor unstable interface... more A statistical model is analyzed for the growth of bubbles in a Rayleigh–Taylor unstable interface. The model is compared to solutions of the full Euler equations for compressible two phase flow, using numerical solutions based on the method of front tracking. The front tracking method has the distinguishing feature of being a predominantly Eulerian method in which sharp interfaces are

Research paper thumbnail of A QMU approach for characterizing the operability limits of air-breathing hypersonic vehicles

Reliability Engineering & System Safety, 2011

The operability limits of a supersonic combustion engine for an air-breathing hypersonic vehicle ... more The operability limits of a supersonic combustion engine for an air-breathing hypersonic vehicle are characterized using numerical simulations and an uncertainty quantification methodology. The time-dependent compressible flow equations with heat release are solved in a simplified configuration. Verification, calibration and validation are carried out to assess the ability of the model to reproduce the flow/thermal interactions that occur when the engine unstarts due to thermal choking. Quantification of Margins and Uncertainty (QMU) is used to determine the safe operation region for a range of fuel flow rates and combustor geometries.

Research paper thumbnail of A two-phase flow model of the Rayleigh-Taylor mixing zone

Physics of Fluids, 1996

The Rayleigh-Taylor instability of an interface separating fluids of distinct density is drivenby... more The Rayleigh-Taylor instability of an interface separating fluids of distinct density is drivenby an acceleration across the interface. Low order statistical moments of fluctuating fluidquantities characterize the hydrodynamics of the mixing zone.A new model is proposed for the momentum coupling between the two phases. Thismodel is validated against computational data for compressible flows, including flows near theincompressible limit. Our main

Research paper thumbnail of An Embedded Boundary Method for Solving the Elliptic And Parabolic Interface Problems and Its application to the Stefan Problem

The embedded boundary method (EBM) on a Cartesian grid developed by Johansen and Colella has been... more The embedded boundary method (EBM) on a Cartesian grid developed by Johansen and Colella has been extended to solve the elliptic/parabolic problems in 2D with an interior boundary (also called elliptic interface, parabolic interface problem). The method is a finite volume method. 2nd order accuracy in L∞ norm is achieved. As its application, a Stefan problem is solved. Problems with

Research paper thumbnail of Numerical Simulations of Free Surface Magnetohydrodynamic Flows

We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) fr... more We have developed a numerical algorithm and performed simulations of magnetohydrodynamic (MHD) free surface flows. The corresponding system of MHD equations is a system of strongly coupled hyperbolic and parabolic/elliptic equations in moving and geometrically complex domains. The hyperbolic system is solved using the front tracking technique for the free fluid interface. Parallel algorithms for solving elliptic and parabolic equations

Research paper thumbnail of A numerical algorithm for MHD of free surface flows at low magnetic Reynolds numbers

Journal of Computational Physics, 2007

We have developed a numerical algorithm and computational software for the study of magnetohydrod... more We have developed a numerical algorithm and computational software for the study of magnetohydrodynamics (MHD) of free surface flows at low magnetic Reynolds numbers. The governing system of equations is a coupled hyperbolic–elliptic system in moving and geometrically complex domains. The numerical algorithm employs the method of front tracking and the Riemann problem for material interfaces, second order Godunov-type hyperbolic

Research paper thumbnail of Dynamic Phase Boundaries for Compressible Fluids

Siam Journal on Scientific Computing, 2008

We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. W... more We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. We model the transition as a tracked jump discontinuity. The emphasis here is on the coupling of the phase transition process to acoustic waves, which is required for the study of cavitation induced by strong rarefaction waves. The robustness of the proposed algorithm is verified by application to various physical regimes.

Research paper thumbnail of Direct Numerical Simulation of Bubbly Flows and Application to Cavitation Mitigation

Journal of Fluids Engineering-transactions of The Asme, 2007

The direct numerical simulation (DNS) method has been used to the study of the linear and shock w... more The direct numerical simulation (DNS) method has been used to the study of the linear and shock wave propagation in bubbly fluids and the estimation of the efficiency of the cavitation mitigation in the container of the Spallation Neutron Source liquid mercury target. The DNS method for bubbly flows is based on the front tracking technique developed for free surface flows. Our front tracking hydrodynamic simulation code FronTier is capable of tracking and resolving topological changes of a large number of interfaces in two-and three-dimensional spaces. Both the bubbles and the fluid are compressible. In the application to the cavitation mitigation by bubble injection in the SNS, the collapse pressure of cavitation bubbles was calculated by solving the Keller equation with the liquid pressure obtained from the DNS of the bubbly flows. Simulations of the propagation of linear and shock waves in bubbly fluids have been performed, and a good agreement with theoretical predictions and experiments has been achieved. The validated DNS method for bubbly flows has been applied to the cavitation mitigation estimation in the SNS. The pressure wave propagation in the pure and the bubbly mercury has been simulated, and the collapse pressure of cavitation bubbles has been calculated. The efficiency of the cavitation mitigation by bubble injection has been estimated. The DNS method for bubbly flows has been validated through comparison of simulations with theory and experiments. The use of layers of nondissolvable gas bubbles as a pressure mitigation technique to reduce the cavitation erosion has been confirmed.

Research paper thumbnail of A TSTT integrated FronTier code and its applications in computational fluid physics

Journal of Physics: Conference Series, 2005

We introduce the FronTier-Lite software package and its adaptation to the TSTT geometry and mesh ... more We introduce the FronTier-Lite software package and its adaptation to the TSTT geometry and mesh entity data interface. This package is extracted from the original front tracking code for general purpose scientific and engineering applications. The package contains a static interface library and a dynamic front propagation library. It can be used in research of different scientific problems. We demonstrate

Research paper thumbnail of A renormalization group scaling analysis for compressible two-phase flow

Physics of Fluids A: Fluid Dynamics, 1993

Computational solutions to the Rayleigh–Taylor fluid mixing problem, as modeled by the two‐fluid ... more Computational solutions to the Rayleigh–Taylor fluid mixing problem, as modeled by the two‐fluid two‐dimensional Euler equations, are presented. Data from these solutions are analyzed from the point of view of Reynolds averaged equations, using scaling laws derived from a ...

Research paper thumbnail of From Cardiac Cells to Genetic Regulatory Networks

Lecture Notes in Computer Science, 2011

One of the fundamental questions in the treatment of ventricular cardiac disorders, such as tachy... more One of the fundamental questions in the treatment of ventricular cardiac disorders, such as tachycardia and fibrillation, is under what circumstances does such a disorder arise? To answer to this question, we develop a multiaffine hybrid automaton (MHA) cardiac-cell model, and restate the original question as one of identification of the parameter ranges under which the MHA model accurately reproduces the disorder. The MHA model is obtained from the minimal cardiac model of one of the authors (Fenton) by first bringing it into the form of a canonical, genetic regulatory network, and then linearizing its sigmoidal switches, in an optimal and global way. By leveraging the Rovergene tool for genetic regulatory networks, we are then able to successfully identify parameter ranges of interest.

Research paper thumbnail of Time dependent anomalous diffusion for flow in multi-fractal porous media

Lecture Notes in Physics, 1992

Macroscopic flow computations are used in the modelilig of most practical porous media flow studi... more Macroscopic flow computations are used in the modelilig of most practical porous media flow studies. These computations require macroscopic or effective flow parameters, describing effective fluid behavior over an integrated range of shorter length scales. This requirement is the ...

Research paper thumbnail of Errors in numerical solutions of spherically symmetric shock physics problems

Contemporary Mathematics, 2005

We seek robust and understandable error models for shock physics simulations. The purpose of this... more We seek robust and understandable error models for shock physics simulations. The purpose of this paper is to explore complications introduced by spherical flow in the analysis of errors in the numerical solution of shock interaction problems. In contrast to the case of planar waves, the spherical waves are not constant in strength between interactions and the solution is not piecewise constant between waves. Nevertheless simple power laws predict the dependence of the solution on the radius. We find that the same power laws predict the evolution of the error, as the error, once formed, propagates according to the same laws as govern the solution structures (i.e. the waves) themselves. We analyze errors in composite wave interaction problems based on the analysis of single interactions and a multi-path scattering formula to combine the effects of errors propagating through the individual interactions.

Research paper thumbnail of Three-Dimensional Front Tracking

Siam Journal on Scientific Computing, 1998

Page 1. THREE-DIMENSIONAL FRONT TRACKING ∗ JAMES GLIMM† , JOHN W. GROVE† , XIAO LIN LI‡ , KEH-MIN... more Page 1. THREE-DIMENSIONAL FRONT TRACKING ∗ JAMES GLIMM† , JOHN W. GROVE† , XIAO LIN LI‡ , KEH-MING SHYUE§ , YANNI ZENG† , AND QIANG ZHANG† SIAM J. SCI. COMPUT. c 1998 Society for Industrial and Applied Mathematics Vol. 19, No. 3, pp. ...

Research paper thumbnail of PROGRAM-AT-A- GLANCE

Research paper thumbnail of A theory of macrodispersion for the scale-up problem

Transport in Porous Media, 1993

Dispersion is the result, observable on large length scales, of events which are random on small ... more Dispersion is the result, observable on large length scales, of events which are random on small length scales. When the length scale on which the randomness operates is not small, relative to the observations, then classical dispersion theory fails. The scale up problem refers to situations in which randomness occurs on all length scales, and for which classical dispersion theory necessarily fails. The purpose of this article is to present non-Fickian, theories of dispersion, which do not assume a scale separation between the randomness and the observed consequences, and which do not assume a single length scale.

Research paper thumbnail of Dynamic Phase Boundaries for Compressible Fluids

SIAM Journal on Scientific Computing, 2008

We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. W... more We present an algorithm for the simulation of dynamic phase transitions in compressible fluids. We model the transition as a tracked jump discontinuity. The emphasis here is on the coupling of the phase transition process to acoustic waves, which is required for the study of cavitation induced by strong rarefaction waves. The robustness of the proposed algorithm is verified by application to various physical regimes.

Research paper thumbnail of Statistical Riemann Problems and a Composition Law for Errors in Numerical Solutions of Shock Physics Problems

SIAM Journal on Scientific Computing, 2004

We seek error models for shock physics simulations that are robust and understandable. The purpos... more We seek error models for shock physics simulations that are robust and understandable. The purpose of this paper is to formulate and validate a composition law to estimate errors in the solutions of composite problems in terms of the errors from simpler ones. We illustrate this idea in a simple context. This paper employs several simplifying assumptions (restriction to one spatial dimension, use of a simplified (gamma law) equation of state, and consideration of a single numerical method). In separate papers we will address the effect of these assumptions.