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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

High-order partitioned spectral deferred correction solvers for multiphysics problems

We present an arbitrarily high-order, conditionally stable, partitioned spectral deferred correction (SDC) method for solving multiphysics problems using a sequence of pre-existing single-physics solvers. This method extends the work in [1], [2], which used implicit-explicit Runge-Kutta methods (IMEX) to build high-order, partitioned multiphysics solvers. We consider a generic multiphysics problem modeled as a system of coupled ordinary differential equations (ODEs), coupled through coupling terms that can depend on the state of each subsystem; therefore the method applies to both a semi-discretized system of partial differential equations (PDEs) or problems naturally modeled as coupled systems of ODEs. The sufficient conditions to build arbitrarily high-order partitioned SDC schemes are derived. Based on these conditions, various of partitioned SDC schemes are designed. The stability of the first-order partitioned SDC scheme is analyzed in detail on a coupled, linear model problem. We show that the scheme is conditionally stable, and under conditions on the coupling strength, the scheme can be unconditionally stable. We demonstrate the performance of the proposed partitioned solvers on several classes of multiphysics problems with moderate coupling strength. They include a stiff linear system of ODEs, advection-diffusion-reaction systems, and fluid-structure interaction problems with both incompressible and compressible flows, where we verify the design order of the SDC schemes and study various stability properties. We also directly compare the accuracy, stability, and cost of the proposed partitioned SDC solver with the partitioned IMEX method in [1], [2] on this suite of test problems. The results suggest that the high-order partitioned SDC solvers are more robust than the partitioned IMEX solvers for the numerical examples considered in this work, while the IMEX methods require fewer implicit solves.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Physics-Informed Deep Neural Networks for Learning Parameters and Constitutive Relationships in Subsurface Flow Problems

In this paper, we present a physics informed deep neural network (DNN) method for estimating parameters and unknown physics (constitutive relationships) in partial differential equation (PDE) models. We use PDEs in addition to measurements to train DNNs to approximate unknown parameters and constitutive relationships as well as states. The proposed approach increases the accuracy of DNN approximations of partially known functions when a limited number of measurements is available and allows for training DNNs when no direct measurements of the functions of interest are available. We employ physics informed DNNs to estimate the unknown space-dependent diffusion coefficient in a linear diffusion equation and an unknown constitutive relationship in a non-linear diffusion equation. For the parameter estimation problem, we assume that partial measurements of the coefficient and states are available and demonstrate that under these conditions, the proposed method is more accurate than state-of-the-art methods. For the non-linear diffusion PDE model with a fully unknown constitutive relationship (i.e., no measurements of constitutive relationship are available), the physics informed DNN method can accurately estimate the non-linear constitutive relationship based on state measurements only. Finally, we demonstrate that the proposed method remains accurate in the presence of measurement noise.

42 ENGINEERING↗
DOE OSTI2017

rHARM: ACCRETION AND EJECTION IN RESISTIVE GR-MHD

Turbulent magnetic diffusivity plays an important role for accretion disks and the launching of disk winds. We have implemented magnetic diffusivity and respective resistivity in the general relativistic MHD code HARM. This paper describes the theoretical background of our implementation, its numerical realization, our numerical tests, and preliminary applications. The test simulations of the new code rHARM are compared to an analytic solution of the diffusion equation and a classical shock tube problem. We have further investigated the evolution of the magnetorotational instability (MRI) in tori around black holes (BHs) for a range of magnetic diffusivities. We find an indication for a critical magnetic diffusivity (for our setup) beyond which no MRI develops in the linear regime and for which accretion of torus material to the BH is delayed. Preliminary simulations of magnetically diffusive thin accretion disks around Schwarzschild BHs that are threaded by a large-scale poloidal magnetic field show the launching of disk winds with mass fluxes of about 50% of the accretion rate. The disk magnetic diffusivity allows for efficient disk accretion that replenishes the mass reservoir of the inner disk area and thus allows for long-term simulations of wind launching for more than 5000 time units.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Demonstrating Computational Equivalence Between Continuous and Discrete Adjoint Methods by Calculating Time-Dependent Adjoint Solutions with Neutron Diffusion Models

The continuous adjoint method and the discrete adjoint method are two alternative approaches used to calculate adjoint solutions for adjoint systems. The continuous adjoint method derives adjoint equations analytically from continuous forward equations and then solves the adjoint equations either analytically or numerically in a discretized form whereas the discrete adjoint method calculates the adjoint solutions directly from the discretized forward equations. With regard to the methodology development and calculation procedure, distinct differences are well recognized between the two methods. For certain reasons, both methods are exclusively preferred and commonly used by different computational communities, but limited studies clarify the connections between the two adjoint methods from either of the communities. Herein, this paper demonstrates the computational equivalence between the continuous and discrete adjoint methods by investigating time-dependent adjoint solutions to the two-group neutron diffusion model in nuclear reactor analysis problems using both methods. Adjoint solutions can be used to estimate system parameters for reactor safety analysis. Appropriate final state conditions for the adjoint systems are specified in both of the methods, and the conditions are clarified with proper physical explanations. With the help of an event-based case study on neutron diffusion models, the accuracy of the time-dependent adjoint fluxes obtained from both methods is verified, and the pros and cons of both adjoint methods are examined. More importantly, the computational equivalence of both methods is demonstrated when they are applied to multigroup neutron diffusion systems. The advantage of calculating time-dependent adjoint fluxes by directly solving time-dependent adjoint systems rather than taking steady-state approximations as in common practice is also demonstrated.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2017

A Least-Squares-Based Weak Galerkin Finite Element Method for Second Order Elliptic Equations

Here, in this article, we introduce a least-squares-based weak Galerkin finite element method for the second order elliptic equation. This new method is shown to provide very accurate numerical approximations for both the primal and the flux variables. In contrast to other existing least-squares finite element methods, this new method allows us to use discontinuous approximating functions on finite element partitions consisting of arbitrary polygon/polyhedron shapes. We also develop a Schur complement algorithm for the resulting discretization problem by eliminating all the unknowns that represent the solution information in the interior of each element. Optimal order error estimates for both the primal and the flux variables are established. An extensive set of numerical experiments are conducted to demonstrate the robustness, reliability, flexibility, and accuracy of the least-squares-based weak Galerkin finite element method. Finally, the numerical examples cover a wide range of applied problems, including singularly perturbed reaction-diffusion equations and the flow of fluid in porous media with strong anisotropy and heterogeneity.

nite element methods↗
NASA NTRS1992

A computer model for one-dimensional mass and energy transport in and around chemically reacting particles, including complex gas-phase chemistry, multicomponent molecular diffusion, surface evaporation, and heterogeneous reaction

Various chemically reacting flow problems highlighting chemical and physical fundamentals rather than flow geometry are presently investigated by means of a comprehensive mathematical model that incorporates multicomponent molecular diffusion, complex chemistry, and heterogeneous processes, in the interest of obtaining sensitivity-related information. The sensitivity equations were decoupled from those of the model, and then integrated one time-step behind the integration of the model equations, and analytical Jacobian matrices were applied to improve the accuracy of sensitivity coefficients that are calculated together with model solutions.

Cho, S. Y.↗
DOE OSTI2015

Extending the diffusion approximation to the boundary using an integrated diffusion model

The widely used diffusion approximation is inaccurate to describe the transport behaviors near surfaces and interfaces. To solve such stochastic processes, an integro-differential equation, such as the Boltzmann transport equation (BTE), is typically required. In this work, we show that it is possible to keep the simplicity of the diffusion approximation by introducing a nonlocal source term and a spatially varying diffusion coefficient. We apply the proposed integrated diffusion model (IDM) to a benchmark problem of heat conduction across a thin film to demonstrate its feasibility. We also validate the model when boundary reflections and uniform internal heat generation are present.

36 MATERIALS SCIENCE↗
DOE OSTI2017

Diffusion in random networks

The ensemble averaging technique is applied to model mass transport by diffusion in random networks. The system consists of an ensemble of random networks, where each network is made of pockets connected by tortuous channels. Inside a channel, fluid transport is assumed to be governed by the one-dimensional diffusion equation. Mass balance leads to an integro-differential equation for the pocket mass density. The so-called dual-porosity model is found to be equivalent to the leading order approximation of the integration kernel when the diffusion time scale inside the channels is small compared to the macroscopic time scale. As a test problem, we consider the one-dimensional mass diffusion in a semi-infinite domain. Because of the required time to establish the linear concentration profile inside a channel, for early times the similarity variable is xt $-$1/4 rather than xt $-$1/2 as in the traditional theory. We found this early time similarity can be explained by random walk theory through the network.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Estimation of unknown variable parameters in moving boundary problems

The problem of estimating unknown variable parameters appearing in moving boundary problems is considered; these are specifically nonlinear diffusion equations defined on a moving spatial domain. A spline-based approximation method that results in a sequence of computationally tractable approximate parameter estimation problems has been developed. A convergence result is proved for a certain class of these moving boundary problems. The paper is concluded with a set of representative numerical examples.

Murphy, K. A.↗
NASA NTRS1999

Optical Flow-Field Techniques Used for Measurements in High-Speed Centrifugal Compressors

The overall performance of a centrifugal compressor depends on the performance of the impeller and diffuser as well as on the interactions occurring between these components. Accurate measurements of the flow fields in each component are needed to develop computational models that can be used in compressor design codes. These measurements must be made simultaneously over an area that covers both components so that researchers can understand the interactions occurring between the two components. Optical measurement techniques are being used at the NASA Lewis Research Center to measure the velocity fields present in both the impeller and diffuser of a 4:1 pressure ratio centrifugal compressor operating at several conditions ranging from design flow to surge. Laser Doppler Velocimetry (LDV) was used to measure the intrablade flows present in the impeller, and the results were compared with analyses obtained from two three-dimensional viscous codes. The development of a region of low throughflow velocity fluid within this high-speed impeller was examined and compared with a similar region first observed in a large low-speed centrifugal impeller at Lewis. Particle Image Velocimetry (PIV) is a relatively new technique that has been applied to measuring the diffuser flow fields. PIV can collect data rapidly in the diffuser while avoiding the light-reflection problems that are often encountered when LDV is used. The Particle Image Velocimeter employs a sheet of pulsed laser light that is introduced into the diffuser in a quasi-radial direction through an optical probe inserted near the diffuser discharge. The light sheet is positioned such that its centerline is parallel to the hub and shroud surfaces and such that it is parallel to the diffuser vane, thereby avoiding reflections from the solid surfaces. Seed particles small enough to follow the diffuser flow are introduced into the compressor at an upstream location. A high-speed charge-coupled discharge (CCD) camera is synchronized to the laser pulse rate; this allows it to capture images of seed particle position that are separated by a small increment in time. A crosscorrelation of a particle's position in two consecutive images provides an estimate of flow velocity and direction. Multiple image pairs obtained in rapid succession at a particular flow condition provide enough measurements for statistical significance. PIV provides simultaneous velocity measurements over the entire plane that is illuminated by the light sheet instead of at a single point, as is the case when LDV is used. PIV has a further advantage in that the laser light pulse can be triggered by an external source such as a high-response pressure transducer. This feature will allow PIV to synchronize flow imaging to physical phenomena such as rotating stall or stall precursor waves. We hope that this technique can be used to obtain images of the flow field during and just prior to stall.

Skoch, Gary J.↗
NASA NTRS2002

Magnetohydrodynamic MACH Code Used to Simulate Magnetoplasmadynamic Thrusters

The On-Board Propulsion program at the NASA Glenn Research Center is utilizing a state of-the-art numerical simulation to model the performance of high-power electromagnetic plasma thrusters. Such thrusters are envisioned for use in lunar and Mars cargo transport, piloted interplanetary expeditions, and deep-space robotic exploration of the solar system. The experimental portion of this program is described in reference 1. This article describes the numerical modeling program used to guide the experimental research. The synergistic use of numerical simulations and experimental research has spurred the rapid advancement of high-power thruster technologies for a variety of bold new NASA missions. From its inception as a U.S. Department of Defense code in the mid-1980's, the Multiblock Arbitrary Coordinate Hydromagnetic (MACH) simulation tool has been used by the plasma physics community to model a diverse range of plasma problems--including plasma opening switches, inertial confinement fusion concepts, compact toroid formation and acceleration, z-pinch implosion physics, laser-target interactions, and a variety of plasma thrusters. The MACH2 code used at Glenn is a time-dependent, two-dimensional, axisymmetric, multimaterial code with a multiblock structure. MACH3, a more recent three-dimensional version of the code, is currently undergoing beta tests. The MACH computational mesh moves in an arbitrary Lagrangian-Eulerian (ALE) fashion that allows the simulation of diffusive-dominated and dispersive-dominated problems, and the mesh can be refined via a variety of adaptive schemes to capture regions of varying characteristic scale. The mass continuity and momentum equations model a compressible viscous fluid, and three energy equations are used to simulate nonthermal equilibrium between electrons, ions, and the radiation field. Magnetic fields are modeled by an induction equation that includes resistive diffusion, the Hall effect, and a thermal source for magnetic fields. Various models of plasma resistivity are included, along with ablation models and multiport circuit solvers. The set of equations is closed using either an ideal gas or real equation of state.

Mikellides, Pavlos G.↗
DOE OSTI2023

A Simplified Approach Based on Cellular Automata for Describing Direct Reduced Iron Production in Different Reducing Conditions

A quick computation approach based on cellular automata is developed and implemented to describe the reduction of iron ore pellets by a mixture of reducing agents featured by different H 2 /CO ratios. The evolution of oxygen concentration inside the pellet is followed from the beginning to the end of contact between reducing agent and pellet. The variation of thermal state of pellets and gas mixture is computed based on their initial temperature, considering the heat involved and the convective heat exchange between pellet and gas mixture. The use of cellular automata and finite‐difference method to solve the diffusion equation point out the absence of any diffusion coefficient value, allowing to make the model fit the experimental trial, because the problem is that it is not ruled just by diffusion but also by the concentration variation of reducing agent inside the pellet due to porosity increasing during reduction. The updating of the reducing agents concentration implies a sharp decrease of oxygen concentration that the cellular automata model considers. The developed model is able to provide the in‐line control of reduction process and could be used to adjust the chemical concentration and temperature of injected reducing agents.

Metallurgy & Metallurgical Engineering↗
DOE OSTI2023

A dynamic variational multiscale method on unstructured meshes for stationary transport problems

Here, this paper presents a variational multiscale (VMS) based finite element method where the stabilization parameter is computed dynamically. The current dynamic procedure takes in a general structure/form of the stabilization parameter with unknown coefficients and computes them dynamically in a local fashion resulting in a dynamic VMS-based finite element method. Thus, a static stabilization parameter with pre-defined coefficients is not needed. A variational Germano identity (VGI) based local procedure suitable for unstructured meshes is developed to perform the dynamic computation in a local fashion. The local VGI based procedure is applied for each interior vertex in the mesh and unknown coefficients are first determined locally at each vertex, and subsequently, for each element a maximum value is taken over the vertices of the element. To make the current procedure practical, a coarser secondary solution is constructed from the primary coarse-scale solution, which is done locally over a patch of elements around each interior vertex. Further, averaging steps are employed to make the local dynamic procedure robust. Currently, the new dynamic VMS formulation is applied to steady problems governed by the advection-diffusion and incompressible Navier-Stokes equations in both 1D and 2D to demonstrate its efficacy and effectiveness.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2016

Benchmark problems for numerical implementations of phase field models

Here, we present the first set of benchmark problems for phase field models that are being developed by the Center for Hierarchical Materials Design (CHiMaD) and the National Institute of Standards and Technology (NIST). While many scientific research areas use a limited set of well-established software, the growing phase field community continues to develop a wide variety of codes and lacks benchmark problems to consistently evaluate the numerical performance of new implementations. Phase field modeling has become significantly more popular as computational power has increased and is now becoming mainstream, driving the need for benchmark problems to validate and verify new implementations. We follow the example set by the micromagnetics community to develop an evolving set of benchmark problems that test the usability, computational resources, numerical capabilities and physical scope of phase field simulation codes. In this paper, we propose two benchmark problems that cover the physics of solute diffusion and growth and coarsening of a second phase via a simple spinodal decomposition model and a more complex Ostwald ripening model. We demonstrate the utility of benchmark problems by comparing the results of simulations performed with two different adaptive time stepping techniques, and we discuss the needs of future benchmark problems. The development of benchmark problems will enable the results of quantitative phase field models to be confidently incorporated into integrated computational materials science and engineering (ICME), an important goal of the Materials Genome Initiative.

36 MATERIALS SCIENCE↗
DOE OSTI2016

The Improved Simple Corner Balance Method and Efforts to Enhance its Computational Performance

The diamond difference (DD) spatial discretization has long been a work horse of the neutron transport community. For nearly as long as DD has been used in neutron transport, it has been observed that DD produces undamped, non-physical angular fluxes in spatially under resolved problems and can fail in the thick diffusion limit. A long list of alternative spatial discretizations, all with better physics properties: accuracy, robustness, and/or preservation of the thick diffusion limit, have been proposed as alternatives to DD. Unfortunately, these alternative spatial discretizations also require significantly more floating point operations (FLOPs) per unknown compared to DD. Historically, neutron transport problems of interest have been able to be resolved sufficiently that DD is accurate enough and FLOPs have been the computational performance bottleneck controlling time to solution. Thus, in practice DD has been and remains a preferred spatial discretization for neutron transport simulations. Trends in computing architecture are leading to a new paradigm where data movement, not FLOPs will control time to solution. This presents an opportunity to improve neutron transport physics by reconsidering more FLOP intensive spatial discretization than DD without incurring a time to solution penalty. In this work, we consider the improved simple corner balance (ISCB) spatial discretization, a unique alternative to DD that has the same memory footprint as DD, and detail efforts to improve its computational performance. The ISCB spatial discretization is a more FLOP intensive spatial discretization than DD with the same memory footprint as DD. Though designed to maximize FLOP intensity, third party libraries such as LAPACK are not tuned for the unique, frequent, small linear algebra needs of neutron transport problems. While hand coding a sparse Gauss elimination is likely to be faster than a dense matrix solve (CM vs. HGE), were LAPACK suitable for small linear algebra problems, we would not have seen a performance increase with decreased numbers of LAPACK calls for the Schur complement solve (SC4 vs. SC1). Significant effort has reduced the relative compute time of ISCB to DD, but on current computer architectures DD is still faster than ISCB. Future work comparing the overall efficiency of ISCB to DD may reveal that while ISCB is slower than DD on current computers, ISCB is more accurate than DD by a factor greater than the compute time slowdown. As new computer architectures become available, we will test our hypothesis that neutron transport simulations will be bandwidth limited, ideally rendering the additional FLOPs required by ISCB to be 'free' [in terms of time to solution]. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2016

Multi-Dimensional, Non-Pyrolyzing Ablation Test Problems

Non-pyrolyzingcarbonaceous materials represent a class of candidate material for hypersonic vehicle components providing both structural and thermal protection system capabilities. Two problems relevant to this technology are presented. The first considers the one-dimensional ablation of a carbon material subject to convective heating. The second considers two-dimensional conduction in a rectangular block subject to radiative heating. Surface thermochemistry for both problems includes finite-rate surface kinetics at low temperatures, diffusion limited ablation at intermediate temperatures, and vaporization at high temperatures. The first problem requires the solution of both the steady-state thermal profile with respect to the ablating surface and the transient thermal history for a one-dimensional ablating planar slab with temperature-dependent material properties. The slab front face is convectively heated and also reradiates to a room temperature environment. The back face is adiabatic. The steady-state temperature profile and steady-state mass loss rate should be predicted. Time-dependent front and back face temperature, surface recession and recession rate along with the final temperature profile should be predicted for the time-dependent solution. The second problem requires the solution for the transient temperature history for an ablating, two-dimensional rectangular solid with anisotropic, temperature-dependent thermal properties. The front face is radiatively heated, convectively cooled, and also reradiates to a room temperature environment. The back face and sidewalls are adiabatic. The solution should include the following 9 items: final surface recession profile, time-dependent temperature history of both the front face and back face at both the centerline and sidewall, as well as the time-dependent surface recession and recession rate on the front face at both the centerline and sidewall. The results of the problems from all submitters will be collected, summarized, and presented at a later conference.

Ablation↗
NASA NTRS1999

Flow/Soot-Formation Interactions in Nonbuoyant Laminar Diffusion Flames

Nonpremixed (diffusion) flames are attractive for practical applications because they avoid the stability, autoignition, flashback, etc. problems of premixed flames. Unfortunately, soot formation in practical hydrocarbon-fueled diffusion flames reduces their attractiveness due to widely-recognized public health and combustor durability problems of soot emissions. For example, more deaths are attributed to the emission of soot (15,000-60,000 deaths annually in the U.S. alone) than any other combustion-generated pollutant. In addition, continuum radiation from soot-containing flames is the principle heat load to combustor components and is mainly responsible for engine durability problems of aircraft and gas turbine engines. As a result, there is considerable interest in controlling both soot concentrations within flames and soot emissions from flames. Thus, the objective of the present investigation is to study ways to control soot formation in diffusion flames by manipulating the mixing process between the fuel and oxidant streams. In order to prevent the intrusion of gravity from masking flow properties that reduce soot formation in practical flames (where effects of gravity are small), methods developed during past work will be exploited to minimize effects of buoyant motion.

Dai, Z.↗
NASA NTRS1954

Heat transfer, diffusion, and evaporation

Although it has long been known that the differential equations of the heat-transfer and diffusion processes are identical, application to technical problems has only recently been made. In 1916 it was shown that the speed of oxidation of the carbon in iron ore depends upon the speed with which the oxygen of the combustion air diffuses through the core of gas surrounding the carbon surface. The identity previously referred to was then used to calculate the amount of oxygen diffusing to the carbon surface on the basis of the heat transfer between the gas stream and the carbon surface. Then in 1921, H. Thoma reversed that procedure; he used diffusion experiments to determine heat-transfer coefficients. Recently Lohrisch has extended this work by experiment. A technically very important application of the identity of heat transfer and diffusion is that of the cooling tower, since in this case both processes occur simultaneously.

GASES - DIFFUSION↗