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DOE OSTI2015

A numerical approach for simulating fluid structure interaction of flexible thin shells undergoing arbitrarily large deformations in complex domains

We present a new numerical methodology for simulating fluid–structure interaction (FSI) problems involving thin flexible bodies in an incompressible fluid. The FSI algorithm uses the Dirichlet–Neumann partitioning technique. The curvilinear immersed boundary method (CURVIB) is coupled with a rotation-free finite element (FE) model for thin shells enabling the efficient simulation of FSI problems with arbitrarily large deformation. Turbulent flow problems are handled using large-eddy simulation with the dynamic Smagorinsky model in conjunction with a wall model to reconstruct boundary conditions near immersed boundaries. The CURVIB and FE solvers are coupled together on the flexible solid–fluid interfaces where the structural nodal positions, displacements, velocities and loads are calculated and exchanged between the two solvers. Loose and strong coupling FSI schemes are employed enhanced by the Aitken acceleration technique to ensure robust coupling and fast convergence especially for low mass ratio problems. The coupled CURVIB-FE-FSI method is validated by applying it to simulate two FSI problems involving thin flexible structures: 1) vortex-induced vibrations of a cantilever mounted in the wake of a square cylinder at different mass ratios and at low Reynolds number; and 2) the more challenging high Reynolds number problem involving the oscillation of an inverted elastic flag. For both cases the computed results are in excellent agreement with previous numerical simulations and/or experiential measurements. Grid convergence tests/studies are carried out for both the cantilever and inverted flag problems, which show that the CURVIB-FE-FSI method provides their convergence. Finally, the capability of the new methodology in simulations of complex cardiovascular flows is demonstrated by applying it to simulate the FSI of a tri-leaflet, prosthetic heart valve in an anatomic aorta and under physiologic pulsatile conditions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2019

QUIC-fire: A fast-running simulation tool for prescribed fire planning

Coupled fire-atmospheric modeling tools are increasingly used to understand the complex and dynamic behavior of wildland fires. Multiple research tools linking combustion to fluid flow use Navier-Stokes numerical solutions coupled to a thermodynamic model to understand fire-atmospheric feedbacks, but these computational fluid dynamics approaches require high-performance computing resources. We present a new simulation tool called QUIC-Fire to rapidly solve these feedbacks by coupling the mature 3-D rapid wind solver QUIC-URB to a physics-based cellular automata fire spread model Fire-CA. QUIC-Fire uses 3-D fuels inputs similar to the CFD model FIRETEC, allowing this tool to simulate effects of fuel structure on local winds and fire behavior. Results comparing fire behavior metrics to the computational fluid dynamic model FIRETEC show strong agreement. As a result, QUIC-Fire is the first tool intended to provide an opportunity for prescribed fire planners to compare, evaluate and design burn plans, including complex ignition patterns and coupled fire atmospheric feedbacks.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2014

Simulation of confined magnetohydrodynamic flows with Dirichlet boundary conditions using a pseudo-spectral method with volume penalization

A volume penalization approach to simulate magnetohydrodynamic (MHD) flows in confined domains is presented. Here the incompressible visco-resistive MHD equations are solved using parallel pseudo-spectral solvers in Cartesian geometries. The volume penalization technique is an immersed boundary method which is characterized by a high flexibility for the geometry of the considered flow. In the present case, it allows to use other than periodic boundary conditions in a Fourier pseudo-spectral approach. The numerical method is validated and its convergence is assessed for two- and three-dimensional hydrodynamic (HD) and MHD flows, by comparing the numerical results with results from literature and analytical solutions. The test cases considered are two-dimensional Taylor–Couette flow, the z-pinch configuration, three dimensional Orszag–Tang flow, Ohmic-decay in a periodic cylinder, three-dimensional Taylor–Couette flow with and without axial magnetic field and three-dimensional Hartmann-instabilities in a cylinder with an imposed helical magnetic field. Finally, we present a magnetohydrodynamic flow simulation in toroidal geometry with non-symmetric cross section and imposing a helical magnetic field to illustrate the potential of the method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

A Two-Stage Decomposition Approach for AC Optimal Power Flow

The alternating current optimal power flow (AC-OPF) problem is critical to power system operations and planning, but it is generally hard to solve due to its nonconvex and large-scale nature. Furthermore, this paper proposes a scalable decomposition approach in which the power network is decomposed into a master network and a number of subnetworks, where each network has its own AC-OPF subproblem. This formulates a two-stage optimization problem and requires only a small amount of communication between the master and subnetworks. The key contribution is a smoothing technique that renders the response of a subnetwork differentiable with respect to the input from the master problem, utilizing properties of the barrier problem formulation that naturally arises when subproblems are solved by a primal-dual interior-point algorithm. Consequently, existing efficient nonlinear programming solvers can be used for both the master problem and the subproblems. The advantage of this framework is that speedup can be obtained by processing the subnetworks in parallel, and it has convergence guarantees under reasonable assumptions. The formulation is readily extended to instances with stochastic subnetwork loads. Numerical results show favorable performance and illustrate the scalability of the algorithm which is able to solve instances with more than 11 million buses.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2013

Two-Level Adaptive Algebraic Multigrid for a Sequence of Problems with Slowly Varying Random Coefficients [Adaptive Algebraic Multigrid for Sequence of Problems with Slowly Varying Random Coefficients]

Our paper proposes an adaptive strategy for reusing a previously constructed coarse space by algebraic multigrid to construct a two-level solver for a problem with nearby characteristics. Furthermore, a main target application is the solution of the linear problems that appear throughout a sequence of Markov chain Monte Carlo simulations of subsurface flow with uncertain permeability field. We demonstrate the efficacy of the method with extensive set of numerical experiments.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

Nonconforming Mesh Refinement for High-Order Finite Elements

In this study, we propose a general algorithm for nonconforming adaptive mesh refinement (AMR) of unstructured meshes in high-order finite element codes. Our focus is on $h$-refinement with a fixed polynomial order. The algorithm handles triangular, quadrilateral, hexahedral, and prismatic meshes of arbitrarily high-order curvature, for any order finite element space in the de Rham sequence. We present a flexible data structure for meshes with hanging nodes and a general procedure to construct the conforming interpolation operator, both in serial and in parallel. The algorithm and data structure allow anisotropic refinement of tensor product elements in two and three dimensions and support unlimited refinement ratios of adjacent elements. We report numerical experiments verifying the correctness of the algorithms and perform a parallel scaling study to show that we can adapt meshes containing billions of elements and run efficiently on 393,000 parallel tasks. Finally, we illustrate the integration of dynamic AMR into a high-order Lagrangian hydrodynamics solver.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2023

A Family of Multi-Dimensional Thermal Radiative Transfer Test Problems

Many thermal radiative transfer (TRT) test problems have been introduced over the years. Here, we will combine the good features of several tests into one new problem. Our goals are to have a multi-dimensional, multi-group TRT problem that stresses the physics and numerics of codes in a realistic way, but the geometry and materials are idealized just enough to be simple to set up in any code. The proposed problem has no connection to any physical experiment; it is simply meant to have a combination of properties that stress the solvers with both the optically thick and thin limits. To achieve this, we are willing to give up any form of analytic solution.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2026

Towards a Verifiable Domain-Specific Language for Hardware-Accelerated Stencils

Defining a domain-specific language (DSL) that supports vector-calculus abstractions eases the porting of partial differential equation (PDE) solvers to specialized architectures. Sufficiently high-level abstractions empower users to express universal laws with sufficient generality that the laws must always hold true within their domain of validity. A broad class of PDE solvers employs stencil-based algorithms, the target domain of Berkeley Lab's stencil accelerator chip co-design project. First released as open-source in January 2026, the Formal software framework lays a foundation for defining an embedded DSL based on composable operators that implement mimetic numerical methods -- stencil algorithms that guarantee satisfaction of discrete versions of important vector calculus theorems. The Formal DSL will be the frontend to a new class of stencil-PDE accelerators developed jointly by LBNL, UHCL, and UC Berkeley through the DOE Competitive Portfolios for Computer Science Project. This offers the potential of an order of magnitude acceleration for this important category of computational methods to serve the DOE mission. Future work on the Formal DSL will facilitate software verification via type-safe templates that enable problem-specific correctness proofs relying upon generic function theory and carefully crafted unit tests.

Rouson, Damian↗

NASA NTRS1986

Efficient solutions of two-dimensional incompressible steady viscous flows

A simple, efficient, and robust numerical technique is provided for solving two dimensional incompressible steady viscous flows at moderate to high Reynolds numbers. The proposed approach employs an incremental multigrid method and an extrapolation procedure based on minimum residual concepts to accelerate the convergence rate of a robust block-line-Gauss-Seidel solver for the vorticity-stream function Navier-Stokes equations. Results are presented for the driven cavity flow problem using uniform and nonuniform grids and for the flow past a backward facing step in a channel. For this second problem, mesh refinement and Richardson extrapolation are used to obtain useful benchmark solutions in the full range of Reynolds numbers at which steady laminar flow is established.

Morrison, J. H.↗

NASA NTRS1988

Efficient solutions of two-dimensional incompressible steady viscous flows

Morrison, J. H.↗

NASA NTRS1988

Zonal techniques for flowfield simulation about aircraft

A technique for performing conservative flowfield calculations on zonal meshes is described. The underlying flow solver is an implicit, upwind finite volume scheme which can incorporate either a perfect gas or an equilibrium air equation of state. Two different approaches which yield identical results, in terms of performing a conservative flux calculation on a zonal interface, are described and compared in terms of numerical efficiency. The capability of the method to handle relatively complex geometries is demonstrated by considering the flowfield about a model SR71 aircraft.

Walters, Robert W.↗

NASA NTRS1990

An implementation of the look-ahead Lanczos algorithm for non-Hermitian matrices, part 2

It is shown how the look-ahead Lanczos process (combined with a quasi-minimal residual QMR) approach) can be used to develop a robust black box solver for large sparse non-Hermitian linear systems. Details of an implementation of the resulting QMR algorithm are presented. It is demonstrated that the QMR method is closely related to the biconjugate gradient (BCG) algorithm; however, unlike BCG, the QMR algorithm has smooth convergence curves and good numerical properties. We report numerical experiments with our implementation of the look-ahead Lanczos algorithm, both for eigenvalue problem and linear systems. Also, program listings of FORTRAN implementations of the look-ahead algorithm and the QMR method are included.

Freund, Roland W.↗

NASA NTRS2016

Least Squares Shadowing Sensitivity Analysis of Chaotic Flow Around a Two-Dimensional Airfoil

Gradient-based sensitivity analysis has proven to be an enabling technology for many applications, including design of aerospace vehicles. However, conventional sensitivity analysis methods break down when applied to long-time averages of chaotic systems. This breakdown is a serious limitation because many aerospace applications involve physical phenomena that exhibit chaotic dynamics, most notably high-resolution large-eddy and direct numerical simulations of turbulent aerodynamic flows. A recently proposed methodology, Least Squares Shadowing (LSS), avoids this breakdown and advances the state of the art in sensitivity analysis for chaotic flows. The first application of LSS to a chaotic flow simulated with a large-scale computational fluid dynamics solver is presented. The LSS sensitivity computed for this chaotic flow is verified and shown to be accurate, but the computational cost of the current LSS implementation is high.

Blonigan, Patrick J.↗

DOE OSTI2022

(Towards) DNS of a Laboratory Lean CH4/H2 Low-Swirl Flame Impinging on an Inclined Wall

Due to downsizing trends, flame-wall interaction (FWI) is increasingly prominent in gas turbines (GTs). FWI has direct consequences on flame stabilization and pollutant emissions, but it is not well understood in turbulent flows representative of GTs. We present results from a direct numerical simulation (DNS) of a turbulent CH4/H2 model GT low-swirl laboratory-scale flame interacting with an inclined wall. The results from the laboratory flame include simultaneous measurements of velocity using stereo particle imaging velocimetry and OHxCH2O planar laser induced fluorescence. The adaptive-mesh refinement solver PeleLMeX is used, with 24-species, 105-reaction reduced Aramco chemical kinetics mechanism. The premixed fuel-air mixture consists of hydrogen-enriched methane with 70% hydrogen volume fraction and 0.4 equivalence ratio. The inflow is prescribed to match experimental measurements at the burner exit. Karlovitz and turbulent Reynolds numbers are 300 and 400, respectively. The simulation and experimental results show excellent agreement. The flame features a bowl-shape stabilization, with a corrugated, continuous flame front at the leading edge, followed by fragmented reaction zones downstream. A large diffuse cloud of CH2O is formed downstream of the quenching point. The simulation results indicate that the cloud of CH2O is the result of incomplete methane combustion, with CH2O "leaking" from the locally quenched reaction zones.The DNS provides fine-grain resolution of turbulence-flame-wall interaction that cannot be captured with experimental measurements. With access to the entire solution vector at each cell of the computational domain, the local quenching.

flame-wall interactions↗

DOE OSTI2021

Source term method for binary neutron stars initial data

The initial condition problem for a binary neutron star system requires a Poisson equation solver for the velocity potential with a Neumann-like boundary condition on the surface of the star. Difficulties that arise in this boundary value problem are: (a) the boundary is not known a priori, but constitutes part of the solution of the problem; (b) various terms become singular at the boundary. In this work, we present a new method to solve the fluid Poisson equation for irrotational/spinning binary neutron stars. The advantage of the new method is that it does not require complex fluid surface fitted coordinates and it can be implemented in a Cartesian grid, which is a standard choice in numerical relativity calculations. This is accomplished by employing the source term method proposed by Towers, where the boundary condition is treated as a jump condition and is incorporated as additional source terms in the Poisson equation, which is then solved iteratively. The issue of singular terms caused by vanishing density on the surface is resolved with an additional separation that shifts the computation boundary to the interior of the star. We present two-dimensional tests to show the convergence of the source term method, and we further apply this solver to a realistic three-dimensional binary neutron star problem. By comparing our solution with the one coming from the initial data solver cocal, we demonstrate agreement to approximately 1%. We report our method can be used in other problems with non-smooth solutions like in magnetized neutron stars.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2025

AMR-Wind: A Performance-Portable, High-Fidelity Flow Solver for Wind Farm Simulations

We present AMR-Wind, a verified and validated high-fidelity computational-fluid-dynamics code for wind farm flows. AMR-Wind is a block-structured, adaptive-mesh, incompressible-flow solver that enables predictive simulations of the atmospheric boundary layer and wind plants. It is a highly scalable code designed for parallel high-performance computing with a specific focus on performance portability for current and future computing architectures, including graphical processing units (GPUs). In this paper, we detail the governing equations, the numerical methods, and the turbine models. Establishing a foundation for the correctness of the code, we present the results of formal verification and validation. The verification studies, which include a novel actuator line test case, indicate that AMR-Wind is spatially and temporally second-order accurate. The validation studies demonstrate that the key physics capabilities implemented in the code, including actuator disk models, actuator line models, turbulence models, and large eddy simulation (LES) models for atmospheric boundary layers, perform well in comparison to reference data from established computational tools and theory. We conclude with a demonstration simulation of a 12-turbine wind farm operating in a turbulent atmospheric boundary layer, detailing computational performance and realistic wake interactions.

17 WIND ENERGY↗

DOE OSTI2022

Verification of MOOSE/Bison's Heat Conduction Solver Using Combined Spatiotemporal Convergence Analysis

Bison is a computational physics code that uses the finite element method to model the thermo-mechanical response of nuclear fuel. Since Bison is used to inform high-consequence decisions, it is important that its computational results are reliable and predictive. One important step in assessing the reliability and predictive capabilities of a simulation tool is the verification process, which quantifies numerical errors in a discrete solution relative to the exact solution of the mathematical model. One step in the verification process—called code verification—ensures that the implemented numerical algorithm is a faithful representation of the underlying mathematical model, including partial differential or integral equations, initial and boundary conditions, and auxiliary relationships. In this paper, the code verification process is applied to spatiotemporal heat conduction problems in Bison. Simultaneous refinement of the discretization in space and time is employed to reveal any potential mistakes in the numerical algorithms for the interactions between the spatial and temporal components of the solution. For each verification problem, the correct spatial and temporal order of accuracy is demonstrated for both first- and second-order accurate finite elements and a variety of time-integration schemes. Furthermore, these results provide strong evidence that the Bison numerical algorithm for solving spatiotemporal problems reliably represents the underlying mathematical model in MOOSE. The selected test problems can also be used in other simulation tools that numerically solve for conduction or diffusion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

NASA NTRS1993

Parallel-vector unsymmetric Eigen-Solver on high performance computers

The popular QR algorithm for solving all eigenvalues of an unsymmetric matrix is reviewed. Among the basic components in the QR algorithm, it was concluded from this study, that the reduction of an unsymmetric matrix to a Hessenberg form (before applying the QR algorithm itself) can be done effectively by exploiting the vector speed and multiple processors offered by modern high-performance computers. Numerical examples of several test cases have indicated that the proposed parallel-vector algorithm for converting a given unsymmetric matrix to a Hessenberg form offers computational advantages over the existing algorithm. The time saving obtained by the proposed methods is increased as the problem size increased.

Nguyen, Duc T.↗