IFIP Advances in Information and Communication Technology, 2012
ABSTRACT Uncertainty Quantification (UQ) for fluid mixing depends on the length scales for observ... more ABSTRACT Uncertainty Quantification (UQ) for fluid mixing depends on the length scales for observation: macro, meso and micro, each with its own UQ requirements. New results are presented here for macro and micro observables. For the micro observables, recent theories argue that convergence of numerical simulations in Large Eddy Simulations (LES) should be governed by space-time dependent probability distribution functions (PDFs, in the present content, Young measures) which satisfy the Euler equation. From a single deterministic simulation in the LES, or inertial regime, we extract a PDF by binning results from a space time neighborhood of the convergence point. The binned state values constitute a discrete set of solution values which define an approximate PDF. The convergence of the associated cumulative distribution func-tions (CDFs) are assessed by standard function space metrics.
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
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
We report significant developments of the FronTier code and applications in science and engineeri... more We report significant developments of the FronTier code and applications in science and engineering. The progress includes the extraction of an independent software library from the front tracking code, robust and accurate locally grid based method, applications to fluid mixing problem, fuel injection jet and fusion pellet injection in a magnetically confined plasma, among other problems.
We outline a program for the study of turbulent mixing of compressible fluids. We emphasize recen... more We outline a program for the study of turbulent mixing of compressible fluids. We emphasize recent progress and steps still to be taken.
Computational solutions to the RayleighTaylor fluid mixing problem, as modeled by the two‐fluid ... more Computational solutions to the RayleighTaylor 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 ...
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.
2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, 2005
High-throughput mass spectrometry and statistical analysis methodologies are promising technologi... more High-throughput mass spectrometry and statistical analysis methodologies are promising technologies to aid the medical diagnostics field by detecting the cancer-related proteomic markers. We propose statistical methods to cull the potential markers by ranking them in relations to their power of separability distinguishing cancerous patients from normal persons or among different cancer stages. To assess the training variability, resampling via bootstrap strategy is adopted to select stable markers which show the potential of a large probability to classify specific groups. Selected marker pattern is validated by a combined classifier. Methods are demonstrated by a colon cancer dataset screened by SELDI technology.
Computational Fluid and Solid Mechanics 2003, 2003
The breakup of injected fuel into spray is of key interest to the design of a fuel efficient, non... more The breakup of injected fuel into spray is of key interest to the design of a fuel efficient, nonpolluting diesel engine. We report preliminary progress on the numerical simulation of diesel fuel injection spray with the front tracking code FronTier. Our simulation design is set to match experiments at ANL, and our present agreement is semi-quantitative. Future efforts will include mesh refinement studies, which will better model the turbulent flow.
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 ...
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.
Dynamics of two-dimensional RayleighTaylor bubbles for fluids with a finite density contrast. [P... more Dynamics of two-dimensional RayleighTaylor bubbles for fluids with a finite density contrast. [Physics of Fluids 15, 2190 (2003)]. Snezhana I. Abarzhi, James Glimm, An-Der Lin. Abstract. We study the motion of a two-dimensional ...
In the context of the classical Rayleigh-Taylor hydrodynamical instability, we examine the much d... more In the context of the classical Rayleigh-Taylor hydrodynamical instability, we examine the much debated question of models for initial conditions and the possible influence of unrecorded long wave length contributions to the instability growth rate .
Zeitschrift Fur Angewandte Mathematik Und Physik - ZAMP, 2002
In this paper we formulate a multiphase model with nonequilibrated temperatures but with equal ve... more In this paper we formulate a multiphase model with nonequilibrated temperatures but with equal velocities and pressures for each species. Turbulent mixing is driven by difiusion in these equations. The closure equations are deflned in part by reference to a more exact chunk mix model developed by the authors and coworkers which has separate pressures, temperatures, and velocities for each species. There are two main results in this paper. The flrst is to identify a thermodynamic constraint, in the form of a process dependence, for pressure equilibrated models. The second is to determine one of the difiusion coe-cients needed for the closure of the equilibrated pressure multiphase ∞ow equations, in the incompressible case. The difiusion coe-cients depend on entrainment times derived from the chunk mix model. These entrainment times are determined here flrst via general formulas and then explicitly for Rayleigh-Taylor and Richtmyer-Meshkov large time asymptotic ∞ows. We also determine...
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. Porous media flow properties are heterogeneous on all length scales. The geological variation on length scales below the observational length scale can be regarded as unknown and unknowable, and thus as a random variable. We develop a systematic theory relating scaling behavior of the geological heterogeneity to the scaling behavior of the fluid dispersivity. Three qualitatively distinct regimes (Fickian, non-Fickian and nonrenormalizable) are found. The theory gives consistent answers within several distinct analytic approximations, and with numerical simulation of the equations of porous media flow. Comparison to field data is made. The use of Kriging to generate constrained ensembles for conditional simulation is discussed.
IFIP Advances in Information and Communication Technology, 2012
ABSTRACT Uncertainty Quantification (UQ) for fluid mixing depends on the length scales for observ... more ABSTRACT Uncertainty Quantification (UQ) for fluid mixing depends on the length scales for observation: macro, meso and micro, each with its own UQ requirements. New results are presented here for macro and micro observables. For the micro observables, recent theories argue that convergence of numerical simulations in Large Eddy Simulations (LES) should be governed by space-time dependent probability distribution functions (PDFs, in the present content, Young measures) which satisfy the Euler equation. From a single deterministic simulation in the LES, or inertial regime, we extract a PDF by binning results from a space time neighborhood of the convergence point. The binned state values constitute a discrete set of solution values which define an approximate PDF. The convergence of the associated cumulative distribution func-tions (CDFs) are assessed by standard function space metrics.
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
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
We report significant developments of the FronTier code and applications in science and engineeri... more We report significant developments of the FronTier code and applications in science and engineering. The progress includes the extraction of an independent software library from the front tracking code, robust and accurate locally grid based method, applications to fluid mixing problem, fuel injection jet and fusion pellet injection in a magnetically confined plasma, among other problems.
We outline a program for the study of turbulent mixing of compressible fluids. We emphasize recen... more We outline a program for the study of turbulent mixing of compressible fluids. We emphasize recent progress and steps still to be taken.
Computational solutions to the RayleighTaylor fluid mixing problem, as modeled by the two‐fluid ... more Computational solutions to the RayleighTaylor 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 ...
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.
2005 IEEE Engineering in Medicine and Biology 27th Annual Conference, 2005
High-throughput mass spectrometry and statistical analysis methodologies are promising technologi... more High-throughput mass spectrometry and statistical analysis methodologies are promising technologies to aid the medical diagnostics field by detecting the cancer-related proteomic markers. We propose statistical methods to cull the potential markers by ranking them in relations to their power of separability distinguishing cancerous patients from normal persons or among different cancer stages. To assess the training variability, resampling via bootstrap strategy is adopted to select stable markers which show the potential of a large probability to classify specific groups. Selected marker pattern is validated by a combined classifier. Methods are demonstrated by a colon cancer dataset screened by SELDI technology.
Computational Fluid and Solid Mechanics 2003, 2003
The breakup of injected fuel into spray is of key interest to the design of a fuel efficient, non... more The breakup of injected fuel into spray is of key interest to the design of a fuel efficient, nonpolluting diesel engine. We report preliminary progress on the numerical simulation of diesel fuel injection spray with the front tracking code FronTier. Our simulation design is set to match experiments at ANL, and our present agreement is semi-quantitative. Future efforts will include mesh refinement studies, which will better model the turbulent flow.
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 ...
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.
Dynamics of two-dimensional RayleighTaylor bubbles for fluids with a finite density contrast. [P... more Dynamics of two-dimensional RayleighTaylor bubbles for fluids with a finite density contrast. [Physics of Fluids 15, 2190 (2003)]. Snezhana I. Abarzhi, James Glimm, An-Der Lin. Abstract. We study the motion of a two-dimensional ...
In the context of the classical Rayleigh-Taylor hydrodynamical instability, we examine the much d... more In the context of the classical Rayleigh-Taylor hydrodynamical instability, we examine the much debated question of models for initial conditions and the possible influence of unrecorded long wave length contributions to the instability growth rate .
Zeitschrift Fur Angewandte Mathematik Und Physik - ZAMP, 2002
In this paper we formulate a multiphase model with nonequilibrated temperatures but with equal ve... more In this paper we formulate a multiphase model with nonequilibrated temperatures but with equal velocities and pressures for each species. Turbulent mixing is driven by difiusion in these equations. The closure equations are deflned in part by reference to a more exact chunk mix model developed by the authors and coworkers which has separate pressures, temperatures, and velocities for each species. There are two main results in this paper. The flrst is to identify a thermodynamic constraint, in the form of a process dependence, for pressure equilibrated models. The second is to determine one of the difiusion coe-cients needed for the closure of the equilibrated pressure multiphase ∞ow equations, in the incompressible case. The difiusion coe-cients depend on entrainment times derived from the chunk mix model. These entrainment times are determined here flrst via general formulas and then explicitly for Rayleigh-Taylor and Richtmyer-Meshkov large time asymptotic ∞ows. We also determine...
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. Porous media flow properties are heterogeneous on all length scales. The geological variation on length scales below the observational length scale can be regarded as unknown and unknowable, and thus as a random variable. We develop a systematic theory relating scaling behavior of the geological heterogeneity to the scaling behavior of the fluid dispersivity. Three qualitatively distinct regimes (Fickian, non-Fickian and nonrenormalizable) are found. The theory gives consistent answers within several distinct analytic approximations, and with numerical simulation of the equations of porous media flow. Comparison to field data is made. The use of Kriging to generate constrained ensembles for conditional simulation is discussed.
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Papers by Adele Glimm