Multiphysics Algorithm Research Articles

Abstract 17617: Toward Improving Diagnosis and Interventional Predictability in Aortic Valve Stenosis Using Computational Modeling

Introduction: Watchful waiting for symptoms or critical hemodynamics to intervene on aortic stenosis (AS) may delay too long. While stress tests can detect symptoms in allegedly asymptomatic AS patients, image-based computations based on advanced modeling techniques can provide critical biomechanical insights. Hypothesis: Advanced computational modeling techniques utilizing patient data backed by high-performance computing can inform a personalized understanding of disease progression, diagnosis, and anticipated post-op hemodynamics to predict interventional efficacy. Methods: A validated in-house Fluid-structure Interaction (FSI) algorithm that allows easy translation of patient-specific anatomies was utilized to perform "virtual stress test" on a moderate AS with increasing LV contraction to predict systolic ejection dynamics under stress. TAVR was virtually implanted and post-op aortic hemodynamics were quantitatively compared with pre-op (diseased) data. Results: Predictions demonstrated that that aortic flow turbulence in moderate AS (Re = 11,700) during exercise (115 bpm) can be similar to severe AS (Re=10,000) at rest (70 bpm) resulting in a greater dissipation losses rising linearly with heart rates. As LV contraction rose, each valve cusp underwent a distinct non-linear rise (>100%) in mechanical stresses that can accelerate calcification. Interestingly, our evaluation revealed that the heterogenous ΔP vs. Q relationship in AS observed clinically can be attributed to a non-linear rise in aortic valve area occurring during mid-systole. Aortic hemodynamics improved post-TAVR by reducing dissipation losses by ~11 fold and restoring near-normal peak-systolic velocity (1.7 m/s) in the ascending aorta. Conclusions: High-performance based multi-physics algorithms incorporating patient data might offer comprehensive biomechanical insights into diagnosis and interventional suitability for aortic valve stenosis.

AMReX: Block-structured adaptive mesh refinement for multiphysics applications

Block-structured adaptive mesh refinement (AMR) provides the basis for the temporal and spatial discretization strategy for a number of Exascale Computing Project applications in the areas of accelerator design, additive manufacturing, astrophysics, combustion, cosmology, multiphase flow, and wind plant modeling. AMReX is a software framework that provides a unified infrastructure with the functionality needed for these and other AMR applications to be able to effectively and efficiently utilize machines from laptops to exascale architectures. AMR reduces the computational cost and memory footprint compared to a uniform mesh while preserving accurate descriptions of different physical processes in complex multiphysics algorithms. AMReX supports algorithms that solve systems of partial differential equations in simple or complex geometries and those that use particles and/or particle–mesh operations to represent component physical processes. In this article, we will discuss the core elements of the AMReX framework such as data containers and iterators as well as several specialized operations to meet the needs of the application projects. In addition, we will highlight the strategy that the AMReX team is pursuing to achieve highly performant code across a range of accelerator-based architectures for a variety of different applications.

On a multiphysics approach to modelling the erosion–enhanced corrosion of low–alloy carbon steel in chloride containing environments

The effect of chloride on erosion-enhanced corrosion was studied experimentally and by a multiphysics algorithm developed to describe the erosion-corrosion interactions. API 5 L X65 steel was exposed to a slurry jet of different chloride content (0.005, 0.05 or 0.5 M) containing silica particles (250–350 μm). An electrochemical-transport-reaction model was used for numerical simulation of polarization curves. Visualization of the flow conditions was also carried out in this work. The effect of erosion on corrosion was found to be well described as a proportionality factor between the kinetics constants of the electrochemical reactions with and without the erodent. The presence of chloride was found to affect the system mainly through increased conductivity of the electrolyte.

Parameter-robust multiphysics algorithms for Biot model with application in brain edema simulation

In this paper, we develop parameter-robust numerical algorithms for Biot model and apply the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model. Based on the reformulation, the Biot model is viewed as a generalized Stokes subproblem combining with a reaction–diffusion subproblem. Solving the two subproblems together or separately leads to a coupled or a decoupled algorithm. We conduct extensive numerical experiments to show that the two algorithms are robust with respect to the key physical parameters. The algorithms are applied to study the brain swelling caused by abnormal accumulation of cerebrospinal fluid in injured areas. The effects of the key physical parameters on brain swelling are carefully investigated. It is observed that the permeability has the biggest influence on intracranial pressure (ICP) and tissue deformation; the Young’s modulus and the Poisson ratio do not affect the maximum value of ICP too much but have big influence on the tissue deformation and the developing speed of brain swelling.

A scalable multiphysics algorithm for massively parallel direct numerical simulations of electrophoretic motion

We introduce a novel coupled algorithm for massively parallel direct numerical simulations of electrophoresis in microfluidic flows. This multiphysics algorithm employs an Eulerian description of fluid and ions, combined with a Lagrangian representation of moving charged particles. The fixed grid facilitates efficient solvers and the employed lattice Boltzmann method can efficiently handle complex geometries. Validation experiments with more than 70 000 time steps are presented, together with scaling experiments with over 4 × 106 particles and 1.96 × 1011 grid cells for both hydrodynamics and electric potential. We achieve excellent performance and scaling on up to 65 536 cores of a current supercomputer.

Parameter Optimization of Robotize Line Scan Thermography for CFRP Composite Inspection

Demands for Composite materials is increasing more and more because of their specific mechanical properties, especially in aerospace industry. Due to the porous structure of composite materials, there is the negligible probability of breaking up and defects in the internal structure. Detection of deep defects is a challenging subject in the field of Non-destructive testing. Due to the large size of composite components in the aerospace industry, line scanning thermography (LST) coupled with a robot arm is used to inspect large composite materials. In this paper, an innovative optimization procedure has been employed using analytical model, 3-D simulation using COMSOL Multiphysics, experimental setup and signal processing algorithms. The goal is to maximize the detection depth and signal to noise value as the criteria to evaluate the inspection quality and performance. the proposed algorithm starts searching to find the optimization variables of robotized LST such as scanning speed, source power and distance considering all technical and mechanical constraints. The optimal values are dependent on the material structure, thermal specifications of the composite, defect shape and infrared camera resolution. Using the proposed optimization algorithm, the detection depth was increased to 3.5 mm in the carbon fiber reinforced polymer and the signal to noise ratio was enhanced to 95%.

The Match Game: Numerical De-Embedding of Field Simulation and Parameter Extraction of Circuit Models for Electromagnetic Structure Using Calibration Techniques

The constantly growing demand for accuracy, efficiency, dependency, and universality in the simulation and circuit modeling of any functional electromagnetic structure-whether devices, circuits, antennas, interconnects, or packaging [1]-[5]-has for decades been the driving force in the development of a number of successful electromagnetic simulation and circuit modeling packages available on the commercial market. In particular, the current trend toward high-density integrations of electromagnetic geometries, from composite-material-based electrical aircraft to nanomaterial-structured electromagnetic sensors, is spurring thedevelopment of various sophisticated multiscale and multiphysics algorithms for rigorous field simulations and design modeling.

Investigating Darcy-scale assumptions by means of a multiphysics algorithm

Multiphysics (or hybrid) algorithms, which couple Darcy and pore-scale descriptions of flow through porous media in a single numerical framework, are usually employed to decrease the computational cost of full pore-scale simulations or to increase the accuracy of pure Darcy-scale simulations when a simple macroscopic description breaks down. Despite the massive increase in available computational power, the application of these techniques remains limited to core-size problems and upscaling remains crucial for practical large-scale applications. In this context, the Hybrid Multiscale Finite Volume (HMsFV) method, which constructs the macroscopic (Darcy-scale) problem directly by numerical averaging of pore-scale flow, offers not only a flexible framework to efficiently deal with multiphysics problems, but also a tool to investigate the assumptions used to derive macroscopic models and to better understand the relationship between pore-scale quantities and the corresponding macroscale variables. Indeed, by direct comparison of the multiphysics solution with a reference pore-scale simulation, we can assess the validity of the closure assumptions inherent to the multiphysics algorithm and infer the consequences for macroscopic models at the Darcy scale. We show that the definition of the scale ratio based on the geometric properties of the porous medium is well justified only for single-phase flow, whereas in case of unstable multiphase flow the nonlinear interplay between different forces creates complex fluid patterns characterized by new spatial scales, which emerge dynamically and weaken the scale-separation assumption. In general, the multiphysics solution proves very robust even when the characteristic size of the fluid-distribution patterns is comparable with the observation length, provided that all relevant physical processes affecting the fluid distribution are considered. This suggests that macroscopic constitutive relationships (e.g., the relative permeability) should account for the fact that they depend not only on the saturation but also on the actual characteristics of the fluid distribution.

Conduction Invariance in Similarity Solutions for Compressible Flow Code Verification

In 1991, Coggeshall published a series of 22 closed-form solutions of the Euler compressible flow equations with a heat conduction term included. A remarkable feature of some of these solutions is invariance with respect to conduction; this phenomenon follows from subtle ancillary constraints wherein a heat flux term is assumed to be either identically zero or nontrivially divergence-free. However, the solutions featuring the nontrivial divergence-free heat flux constraint can be shown to be incomplete, using a well-known result most commonly encountered in elementary electrostatic theory. With this result, the application of the divergence operator to the heat flux distributions exhibited by many of the solutions yields a delta function source term instead of identically zero. In theory, the relevant solutions will be conduction invariant only if the appropriate source term is included. This result has important implications for the use of the Coggeshall similarity solutions as code verification test problems for simulation codes featuring coupled compressible fluid flow and heat conduction processes. Computational reproduction of the conduction invariance property represents a conceptually simple check for verifying the robustness of a multiphysics algorithm. In this work, it is demonstrated in the context of various computational instantiations of Coggeshall solution #8 (Cog8) that to maintain any semblance of conduction invariance, a heat source term must be included even with a simple nonlinear heat conduction process. The efficacy of the heat source term is shown to depend not only on values of the various free parameters included in the Coggeshall mathematical model but also the representation of heat sources in multiphysics simulation codes of interest.

Object-Oriented/Data-Oriented Design of a Direct Simulation Monte Carlo Algorithm

National Aeronautics and Space Administration has been investing in the development of a new code, the Multiphysics Algorithm with Particles, to incorporate recent developments in direct simulation Monte Carlo algorithms and improve physical realism, time to solution, and expand the range of usefulness of National Aeronautics and Space Administration direct simulation Monte Carlo codes (in both velocity space and altitude). The Multiphysics Algorithm with Particles is an object-oriented/data-oriented code written in C++. Object-oriented codes are likely the most flexible and efficient approach for the development of new algorithms and physics modules due to their inherent modularity. However, computational efficiency is an equally critical component of software design that must be considered, which is why data-oriented design becomes important. The focus of the development of the Multiphysics Algorithm with Particles thus far has been on the creation of efficient particle data structures, the inclusion of gas models, and the ability to dynamically adapt a simulation. Future work will focus on more efficient grid structures and parallel computing strategies. The new software is evaluated in the current study with regard to 1) software design and extensibility, 2) accuracy of solution, and 3) efficiency of solution. For each category, comparisons will be made against legacy software to identify the relative merits of each software package. For software design and extensibility, the details of the Software Engineering Plan for the Multiphysics Algorithm with Particles will be presented. For accuracy of solution, comparisons will be made to test cases from the literature. Speed comparisons are made between the Multiphysics Algorithm with Particles and the current production direct simulation Monte Carlo code at National Aeronautics and Space Administration, the direct simulation Monte Carlo Analysis Code, for both serial and parallel implementations. More importantly, though, are the automated grid, time step, and surface temperature adaptation algorithms included in the Multiphysics Algorithm with Particles. The user can now specify the simulation initial conditions and begin the solution one time, and the Multiphysics Algorithm with Particles automatically adapts the solution and determines when the final solution has been reached.

Efficient Multiphysics Coupling for Fast Burst Reactors in Slab Geometry

An efficient neutron transport-based multiphysics coupling algorithm is developed to model fast-burst reactor dynamics. It extends the previously developed tightly coupled implicit-explicit (IMEX) multiphysics algorithm based on neutron diffusion and linear mechanics to follow the dynamic time scale of the problem. The diffusion model is not expected to adequately represent the neutronic behavior of the system due its small size. The transport effects are incorporated using the moment-based acceleration concept. This concept enables us to isolate the angular flux from the coupled multiphysics system by using a consistently discretized lower-order system for the scalar flux in the coupling equations, thus helping to mitigate the increased numerical burden associated with a neutron transport model. Solution of a representative slab model demonstrates the difference between diffusion and transport models and also demonstrates second-order convergence in the coupled simulation with the combination of the moment-based acceleration concept and the IMEX algorithm.

Parallel Algorithms and Software for Nuclear, Energy, and Environmental Applications. Part II: Multiphysics Software

AbstractThis paper is the second part of a two part sequence on multiphysics algorithms and software. The first [1] focused on the algorithms; this part treats the multiphysics software framework and applications based on it. Tight coupling is typically designed into the analysis application at inception, as such an application is strongly tied to a composite nonlinear solver that arrives at the final solution by treating all equations simultaneously. The application must also take care to minimize both time and space error between the physics, particularly if more than one mesh representation is needed in the solution process. This paper presents an application framework that was specifically designed to support tightly coupled multiphysics analysis. The Multiphysics Object Oriented Simulation Environment (MOOSE) is based on the Jacobian-free Newton-Krylov (JFNK) method combined with physics-based preconditioning to provide the underlying mathematical structure for applications. The report concludes with the presentation of a host of nuclear, energy and environmental applications that demonstrate the efficacy of the approach and the utility of a well-designed multiphysics framework.

Development of a Self-Consistent Truly Multiphysics Algorithm Based Upon the Courant-Insensitive Space–Time Conservation-Element Solution-Element Method

This paper reports on the theoretical aspects and current development status of a self-consistent truly multiphysics algorithm. The algorithm is based upon the Courant-insensitive space-time conservation-element solution-element methodology. Previous attempts for electromagnetic solutions have applicability only in constant material domains with PEC boundary conditions. This paper reports on the extension of this algorithm for the solution of the generalized Maxwell equations, including linear-dispersive materials. The numerical solution is shown to be extremely accurate on highly nonuniform meshes and reduces to the classical Yee FDTD error properties in the uniform Cartesian grid limit. Validation problems and comparison with the ubiquitous baseline FDTD algorithm will be presented in 1-D (2-D space-time). Results show that the second-order CESE method has an accuracy equivalent to fourth-sixth order FDTD for equal grids with highly discontinuous coefficients (e.g., permittivity).

Tightly Coupled Multiphysics Algorithms for Pebble Bed Reactors

We have developed a tightly coupled multiphysics simulation tool for the pebble bed reactor (PBR) concept, a specific type of very high temperature gas-cooled reactor. The simulation tool PRONGHORN takes advantage of the Multiphysics Object-Oriented Simulation Environment library and is capable of solving multidimensional thermal-fluid and neutronics problems implicitly with a Newton-based approach. Expensive Jacobian matrix formation is alleviated via the Jacobian-free Newton-Krylov method, and physics-based preconditioning is applied to minimize Krylov iterations. Motivation for the work is provided via analysis and numerical experiments on simpler multiphysics reactor models. We then provide detail of the physical models and numerical methods in PRONGHORN. Finally, PRONGHORN’s algorithmic capability is demonstrated on a number of PBR test cases.

Parallel multiphysics algorithms and software for computational nuclear engineering

There is a growing trend in nuclear reactor simulation to consider multiphysics problems. This can be seen in reactor analysis where analysts are interested in coupled flow, heat transfer and neutronics, and in fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry. These more ambitious simulations usually motivate some level of parallel computing. Many of the coupling efforts to date utilize simple code coupling or first-order operator splitting, often referred to as loose coupling. While these approaches can produce answers, they usually leave questions of accuracy and stability unanswered. Additionally, the different physics often reside on separate grids which are coupled via simple interpolation, again leaving open questions of stability and accuracy. Utilizing state of the art mathematics and software development techniques we are deploying next generation tools for nuclear engineering applications. The Jacobian-free Newton-Krylov (JFNK) method combined with physics-based preconditioning provide the underlying mathematical structure for our tools. JFNK is understood to be a modern multiphysics algorithm, but we are also utilizing its unique properties as a scale bridging algorithm. To facilitate rapid development of multiphysics applications we have developed the Multiphysics Object-Oriented Simulation Environment (MOOSE). Examples from two MOOSE-based applications: PRONGHORN, our multiphysics gas cooled reactor simulation tool and BISON, our multiphysics, multiscale fuel performance simulation tool will be presented.

Multi-physics modeling of flow and transport in porous media using a downscaling approach

Multi-phase flow and transport processes generally occur on different spatial and temporal scales. Very often also, within a physical system, they vary in space meaning that different kinds of processes might take place in different parts of the system. In order to account for the variety of processes and to take their scale-dependence into account, the development of multi-scale multi-physics techniques can be envisaged. We extend a recently developed multi-scale multi-physics algorithm by Niessner and Helmig [Niessner J, Helmig R. Multi-scale modeling of three-phase–three-component processes in heterogeneous porous media. Adv Water Resour 2007;11(30):2309–25] where concentration equations were solved in a small part of the domain on a fine scale while pressure and saturation distribution were solved for in the whole physical system. While the saturation equation was upscaled to a coarser scale the pressure equation was still solved time-implicitly and on a fine scale. The new extension of this work is the upscaling of the pressure equation also. Where needed a downscaling approach provides fine-scale velocities. In this technical note, comparisons of the extended algorithm to the original one and to a fine-scale reference solution are shown. The major benefits of this extension are more flexibility with respect to the choice of scale and computational efficiency (the time-implicit solution of the fine-scale pressure equation is very costly) while maintaining a high accuracy.

A fast 3D particle method for the simulation of buoyant flow

This paper describes progress in several areas related to three-dimensional vortex methods and their application to multiphysics problems. The first is the solution of a generic scalar transport equation by advecting and diffusing the scalar gradient along a particle trajectory and onto a mesh, respectively, and recovering the scalar values using a Biot–Savart-like summation. The second is the accurate, high-resolution calculation of the velocity gradient using a fast treecode, which avoids using kinematic relations between the evolution of the gradients and the distortion of the flow map. The same tree structure is used to compute all the variables of interest and those required during the integration of the governing equations. Next, we apply our modified interpolation kernel algorithm for treating diffusion and remeshing to maintain long time accuracy. The coupling between vorticity transport and that of a dynamic scalar, in this case the temperature or density in a gravitational field, is manifested by the generation of vorticity. We demonstrate the performance of the multiphysics algorithm by solving a number of buoyant flow problems.

Hybrid Simulations of Reaction-Diffusion Systems in Porous Media

Hybrid or multiphysics algorithms provide an efficient computational tool for combining micro- and macroscale descriptions of physical phenomena. Their use becomes imperative when microscale descriptions are too computationally expensive to be conducted in the whole domain, while macroscale descriptions fail in a small portion of the computation domain. We present a hybrid algorithm to model a general class of reaction-diffusion processes in granular porous media, which includes mixing-induced mineral precipitation on, or dissolution of, the porous matrix. These processes cannot be accurately described using continuum (Darcy-scale) models. The pore-scale/Darcy-scale hybrid is constructed by coupling solutions of the reaction-diffusion equations (RDE) at the pore scale with continuum Darcy-level solutions of the averaged RDEs. The resulting hybrid formulation is solved numerically by employing a multiresolution meshless discretization based on the smoothed particle hydrodynamics method. This ensures seamless noniterative coupling of the two components of the hybrid model. Computational examples illustrate the accuracy and efficiency of the hybrid algorithm.