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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

An energy-conserving and asymptotic-preserving charged-particle orbit implicit time integrator for arbitrary electromagnetic fields

Here we present a new implicit asymptotic preserving time integration scheme for charged-particle orbit computation in arbitrary electromagnetic fields. The scheme is built on the Crank-Nicolson integrator and continues to recover full-orbit motion in the small time-step limit, but also recovers all the first-order guiding center drifts as well as the correct gyroradius when stepping over the gyration time-scale. In contrast to previous efforts in this direction, the new scheme also features exact energy conservation. In the derivation of the scheme, we find that a new numerical time-scale is introduced. This scale is analyzed and the resulting restrictions on time-step are derived. Based on this analysis, we develop an adaptive time-stepping strategy the respects these constraints while stepping over the gyration scale when physically justified. It is shown through numerical tests on single-particle motion that the scheme's energy conservation property results in tremendous improvements in accuracy, and that the scheme is able to transition smoothly between magnetized and unmagnetized regimes as a result of the adaptive time-stepping.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Full time-dependent SOLPS-ITER simulation of the SPARC tokamak: actuator design for particle and divertor condition control *

Abstract This paper presents the application of full time-dependent SOLPS-ITER simulations for actuator design in the SPARC tokamak. This study employs both the EIRENE module, a neutral solver, and the B2.5 plasma module in a time-dependent mode. This is in contrast to most SOLPS simulations, which focus on steady-state solutions, where the neutral distribution is evolved without any time limit or for a time step of 1 ⋅ 10 − 3 second, which is several orders of magnitude larger than the fluid plasma time step. The time-dependent EIRENE was tested with a fixed B2.5 background and compared with a simple conductance based model in a simplified pump chamber geometry. This comparison aimed to verify the reliability of the neutral relaxation timescale derived from the time-dependent EIRENE. Subsequently, a full time-dependent simulation was performed in a realistic geometry, with the Monte-Carlo neutral time step synchronized with the plasma fluid time step. The numerical setup of the code, including relative time steps and the size of the census data used to store Monte-Carlo particle information is considered. The full-time dependent simulations are then applied to inform the design of the SPARC louver structure, which affects divertor plasma parameters by regulating the neutral conductance from the divertor to the pump. The response of the plasma and neutral parameters was captured on a timescale that enables the design of the actuator to consider time-dependent control capability. It was found that changing the louver opacity has an equivalent effect as varying the gas throughput via puff actuation. Therefore, equivalent divertor plasma conditions can be obtained from both actuators, while the neutral pressure distribution in the pump and divertor differs for each actuator.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

CFL Optimized Forward–Backward Runge–Kutta Schemes for the Shallow-Water Equations

Abstract We present the formulation and optimization of a Runge–Kutta-type time-stepping scheme for solving the shallow-water equations, aimed at substantially increasing the effective allowable time step over that of comparable methods. This scheme, called FB-RK(3,2), uses weighted forward–backward averaging of thickness data to advance the momentum equation. The weights for this averaging are chosen with an optimization process that employs a von Neumann–type analysis, ensuring that the weights maximize the admittable Courant number. Through a simplified local truncation error analysis and numerical experiments, we show that the method is at least second-order in time for any choice of weights and exhibits low dispersion and dissipation errors for well-resolved waves. Further, we show that an optimized FB-RK(3,2) can take time steps up to 2.8 times as large as a popular three-stage, third-order strong stability-preserving Runge–Kutta method in a quasi-linear test case. In fully nonlinear shallow-water test cases relevant to oceanic and atmospheric flows, FB-RK(3,2) outperforms SSPRK3 in admittable time step by factors roughly between 1.6 and 2.2, making the scheme approximately twice as computationally efficient with little to no effect on solution quality. Significance Statement The purpose of this work is to develop and optimize time-stepping schemes for models relevant to oceanic and atmospheric flows. Specifically, for the shallow-water equations we optimize for schemes that can take time steps as large as possible while retaining solution quality. We find that our optimized schemes can take time steps between 1.6 and 2.2 times larger than schemes that cost the same number of floating point operations, translating directly to a corresponding speedup. Our ultimate goal is to use these schemes in climate-scale simulations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Fast Quasi-Static Time-Series Simulation for Accurate PV Inverter Semiconductor Fatigue Analysis with a Long-Term Solar Profile

Power system simulations with long-term data typically have large time steps varying from one second to a few minutes. However, for PV inverter semiconductors, the minimum thermal stress cycle occurs over the fundamental grid frequency (50 or 60 Hz). This requires the time step of the fatigue simulation to be around 100 µs. This small time step requires long computation times to process yearly power production profiles. This paper proposes a fast fatigue simulation for inverter semiconductors using the quasi-static time series (QSTS) simulation concept. The proposed simulation calculates the steady state of the semiconductor junction temperature by using a Fast Fourier Transform (FFT). The small thermal cycling during a switching period and even over the fundamental waveform is disregarded to further accelerate the simulation speed. The resulting time step of the fatigue simulation is 15 minutes, which is consistent with the solar dataset. The error of the proposed simulation is 0.16% compared to the fatigue simulation results using the complete thermal stress profile. A PV inverter that responds to a Transactive Energy System (TES) is simulated to demonstrate the use of the proposed fatigue simulation. The proposed simulation has the potential to co-simulate with system level simulation tools that also adopt the QSTS concept.

Liu, Yunting↗
DOE OSTI2022

Accelerated Probabilistic Marching Cubes by Deep Learning for Time-Varying Scalar Ensembles

Visualizing the uncertainty of ensemble simulations is challenging due to the large size and multivariate and temporal features of en-semble data sets. One popular approach to studying the uncertainty of ensembles is analyzing the positional uncertainty of the level sets. Probabilistic marching cubes is a technique that performs Monte Carlo sampling of multivariate Gaussian noise distributions for positional uncertainty visualization of level sets. However, the technique suffers from high computational time, making interactive visualization and analysis impossible to achieve. This paper introduces a deep-learning-based approach to learning the level-set uncertainty for two-dimensional ensemble data with a multivariate Gaussian noise assumption. We train the model using the first few time steps from time-varying ensemble data in our workflow. We demonstrate that our trained model accurately infers uncertainty in level sets for new time steps and is up to 170X faster than that of the original probabilistic model with serial computation and 10X faster than that of the original parallel computation.

Han, Mengjiao↗
DOE OSTI2023

Particle-in-cell Simulations of Relativistic Magnetic Reconnection with Advanced Maxwell Solver Algorithms

Abstract Relativistic magnetic reconnection is a nonideal plasma process that is a source of nonthermal particle acceleration in many high-energy astrophysical systems. Particle-in-cell (PIC) methods are commonly used for simulating reconnection from first principles. While much progress has been made in understanding the physics of reconnection, especially in 2D, the adoption of advanced algorithms and numerical techniques for efficiently modeling such systems has been limited. With the GPU-accelerated PIC code WarpX, we explore the accuracy and potential performance benefits of two advanced Maxwell solver algorithms: a nonstandard finite-difference scheme (CKC) and an ultrahigh-order pseudo-spectral method (PSATD). We find that, for the relativistic reconnection problem, CKC and PSATD qualitatively and quantitatively match the standard Yee-grid finite-difference method. CKC and PSATD both admit a time step that is 40% longer than that of Yee, resulting in a ∼40% faster time to solution for CKC, but no performance benefit for PSATD when using a current deposition scheme that satisfies Gauss’s law. Relaxing this constraint maintains accuracy and yields a 30% speedup. Unlike Yee and CKC, PSATD is numerically stable at any time step, allowing for a larger time step than with the finite-difference methods. We found that increasing the time step 2.4–3 times over the standard Yee step still yields accurate results, but it only translates to modest performance improvements over CKC, due to the current deposition scheme used with PSATD. Further optimization of this scheme will likely improve the effective performance of PSATD.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

A Semi-Analytical Solution Approach for Solving Constant-Coefficient First-Order Partial Differential Equations

Simulation and control of many dynamic systems involve solving partial differential equations (PDE). This letter proposes a semi-analytical solution (SAS) approach for fast and high-quality solution of first-order PDEs. The region of interest of the studied PDE is divided into a grid, and an SAS is derived for each grid cell in the form of the multivariate polynomials, of which the coefficients are identified using initial value and boundary value conditions. The solutions are solved in a “time-stepping” manner, i.e. within one time step, the coefficients of the SAS are identified and the initial value of the next time step is evaluated. This approach achieves a significantly larger grid cell than the widely used finite difference method, and thus enhances the computational efficiency significantly. Furthermore, the simulation result on the natural gas pipeline model demonstrates the advantages of SAS in accuracy and computational efficiency.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Accelerating phase field simulations through a hybrid adaptive Fourier neural operator with U-net backbone

Prolonged contact between a corrosive liquid and metal alloys can cause progressive dealloying. For one such process as liquid-metal dealloying (LMD), phase field models have been developed to understand the mechanisms leading to complex morphologies. However, the LMD governing equations in these models often involve coupled non-linear partial differential equations (PDE), which are challenging to solve numerically. In particular, numerical stiffness in the PDEs requires an extremely refined time step size (on the order of 10 -12 s or smaller). This computational bottleneck is especially problematic when running LMD simulation until a late time horizon is required. This motivates the development of surrogate models capable of leaping forward in time, by skipping several consecutive time steps at-once. In this paper, we propose a U-shaped adaptive Fourier neural operator (U-AFNO), a machine learning (ML) based model inspired by recent advances in neural operator learning. U-AFNO employs U-Nets for extracting and reconstructing local features within the physical fields, and passes the latent space through a vision transformer (ViT) implemented in the Fourier space (AFNO). We use U-AFNOs to learn the dynamics of mapping the field at a current time step into a later time step. We also identify global quantities of interest (QoI) describing the corrosion process (e.g., the deformation of the liquid-metal interface, lost metal, etc.) and show that our proposed U-AFNO model is able to accurately predict the field dynamics, in spite of the chaotic nature of LMD. Most notably, our model reproduces the key microstructure statistics and QoIs with a level of accuracy on par with the high-fidelity numerical solver, while achieving a significant 11, 200 × speed-up on a high-resolution grid when comparing the computational expense per time step. Finally, we also investigate the opportunity of using hybrid simulations, in which we alternate forward leaps in time using the U-AFNO with high-fidelity time stepping. We demonstrate that while advantageous for some surrogate model design choices, our proposed U-AFNO model in fully auto-regressive settings consistently outperforms hybrid schemes.

36 MATERIALS SCIENCE↗
DOE OSTI2021

HyPerPy (Hydrogen Extraction and Parabolic Trough Plant Performance Models using Python) [SWR-21-53]

The HyPerPy package consists of three scripts: 1) Model for Hydrogen Tracking in Parabolic Trough Power Plants, 2) Model for Receiver Performance, and 3) Model for Hydrogen Extraction Process. The power plant model (1) tracks hydrogen generation and transport within the circulating heat transfer fluid (HTF) of the power plant. This script is a transient, initial value simulation, in which the hydrogen concentration in the circulating HTF is 0 moles per cubic meter everywhere at time 0 seconds. Hydrogen concentration is calculated at discrete locations within the circulating HTF with 4-second time resolution. During each time step, the change in hydrogen concentration due to hydrogen generation and permeation is calculated for each location according to the local HTF temperature, vessel or piping properties, hydrogen concentration and partial pressure. This model predicts hourly hydrogen concentrations for typical operating days in the spring, summer, fall, and winter seasons. Data is used to create hourly mappings of hydrogen concentrations for a typical operating year. The receiver model (2) uses a 1-hour time step to estimate getter loading and annulus pressure. For each time step, the model uses HTF and ambient temperature data to estimate absorber tube, bellows, and getter temperatures for the time step. In addition, the model uses hourly HTF hydrogen concentrations that are generated by the power plant model (1), and annulus hydrogen pressure from the previous time step. With these data, the model calculates the moles of hydrogen permeating across the absorber tube and bellows during the time step. The net change in moles hydrogen is added or subtracted from the getter loading for the previous time step, and the hydrogen pressure is re-calculated based on getter loading and temperature. The model uses this algorithm to simulate hydrogen permeation and loading 24 hours per day, 365 days per year using seasonal temperature data. The model repeats these calculations for 25 years to create a mapping of receiver getter loading and annulus hydrogen pressure for four seasons of each year. The model for hydrogen extraction (3) estimates hydrogen extraction rates for a specific separation module configuration. The rate depends primarily on membrane area, vacuum pump performance, headspace gas flowrate to the membrane, and headspace gas hydrogen partial pressure. This model has two versions. The steady-state version predicts hydrogen extraction rates when the module is operating in separation mode. The dynamic version predicts hydrogen transfer through the membrane when the module is operating in sensor mode. The steady-state version is used with the plant model (1) to predict hydrogen partial pressures in the power plant when the extraction process is operating.

Glatzmaier, Gregory↗
DOE OSTI2021

Cloud Process Coupling and Time Integration in the E3SM Atmosphere Model

Abstract In this study, we find significant sensitivity to the choice of time step for the Energy Exascale Earth System Model's atmospheric component, leading to large decreases in the magnitude of cloud forcing when the time step is reduced to 10 s. Reducing the time step size for the microphysics increases precipitation, leading to a drying of the atmosphere and an increase in surface evaporation. This effect is amplified when the microphysics is substepped together with other cloud physics processes. Coupling the model's dynamics and physics more frequently reduces cloud fraction at lower altitudes, while producing more cloud liquid at higher altitudes. Reducing the deep convection time step also reduces low cloud mass and cloud fraction. Together, these results suggest that cloud physics in a global circulation model can depend strongly on time step and, in particular, on the frequency with which cloud‐related processes are coupled with each other and with the model dynamics.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Accurately simulating nine-dimensional phase space of relativistic particles in strong fields

Next-generation high-power laser systems that can be focused to ultra-high intensities exceeding 10 23 W/cm 2 are enabling new physics regimes and applications. The physics of how these lasers interact with matter is highly nonlinear, relativistic, and can involve lowest-order quantum effects. The current tool of choice for modeling these interactions is the particle-in-cell (PIC) method. In the presence of strong electromagnetic fields, the motion of charged particles and their spin is affected by radiation reaction (either the semi-classical or the quantum limit). Standard (PIC) codes usually use Boris or similar operator-splitting methods to advance the particles in standard phase space. These methods have been shown to require very small time steps in the strong-field regime in order to obtain accurate results. In addition, some problems require tracking the spin of particles, which creates a nine-dimensional (9D) particle phase space, i.e., (x, u, s). Therefore, numerical algorithms that enable high-fidelity modeling of the 9D phase space in the strong-field regime (where both the spin and momentum evolution are affected by radiation reaction) are desired. Here we present a new particle pusher that works in 9D and 6D phase space (i.e., with and without spin) based on analytical rather than leapfrog solutions to the momentum and spin advance from the Lorentz force, together with the semi-classical form of radiation reaction in the Landau-Lifshitz equation and spin evolution given by the Bargmann-Michel-Telegdi equation. Analytical solutions for the position advance are also obtained, but these are not amenable to the staggering of space and time in standard PIC codes. These analytical solutions are obtained by assuming a locally uniform and constant electromagnetic field during a time step. The solutions provide the 9D phase space advance in terms of a particle's proper time, and a mapping is used to determine the proper time step duration for each particle as a function of the lab frame time step. Due to the analytical integration of particle trajectory and spin orbit, the constraint on the time step needed to resolve trajectories in ultra-high fields can be greatly reduced. The time step required in a PIC code for accurately advancing the fields may provide additional constraints. We present single-particle simulations to show that the proposed particle pusher can greatly improve the accuracy of particle trajectories in 6D or 9D phase space for given laser fields. We have implemented the new pusher into the PIC code Osiris. Example simulations show that the proposed pusher provides improvement for a given time step. A discussion on the numerical efficiency of the proposed pusher is also provided.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Dataset for manuscript "Consequences of the failure of equipartition for the p-V behavior of liquid water and the hydration free energy components of a small protein"

Previously, we showed that in the molecular dynamics simulation of a rigid model of water it is necessary to use an integration time-step dt that is less than or equal to 0.5 fs to ensure equipartition between translational and rotational modes. We extended that study in the NVT ensemble to NpT conditions and to an aqueous protein. We study neat liquid water with the rigid, SPC/E model and the protein BBA (PDB ID: 1FME) solvated in the rigid, TIP3P model. We examined integration time-steps ranging from 0.5 fs to 4.0 fs for various thermostat plus barostat combinations. We find that a small time-step, dt, is necessary to ensure consistent prediction of the simulation volume. Hydrogen mass repartitioning alleviates the problem somewhat, but is ineffective for the typical time-step used with this approach. The compressibility, a measure of volume fluctuations, is seen to be sensitive to dt. Using the mean volume estimated from the NpT simulation, we examined the electrostatic and van der Waals contribution to the hydration free energy of the protein in the NVT ensemble. These contributions are also sensitive to dt. In going from a time-step of 2 fs to a time-step of 0.5 fs, the change in the net electrostatic plus van der Waals contribution to the hydration of BBA is already in excess of the folding free energy reported for this protein. The data-set contains the simulation metadata and log files that support the claims noted above.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Gridded Sub-daily Climate Forcings for North America Based on Daymet and ERA5 (Daymet-ERA5)

To support high spatial and temporal resolution land surface modeling, this dataset provides hourly time step historic weather forcing at 1-km spatial resolution for the entire North America. The latest Daymet V4 data provides gridded historic daily weather observations at 1-km spatial resolution from 1980 to 2024. Using sub-daily temporal information from the ECMWF ERA5 reanalysis, Daymet was further temporally downscaled to hourly time steps and provided in the format required for land surface model simulations. The process of temporal downscaling preserves the relative magnitude in each hourly time step from ERA5 while maintaining the total and average values from Daymet for each day. This results in a blended 1980-2024 Daymet-ERA5 dataset. Available variables include surface air temperature, precipitation, specific humidity, shortwave and longwave radiation, wind speed, and pressure. These data can be used as a high-resolution meteorological forcing dataset to support high-resolution land surface modeling where accurate meteorological forcing datasets built from historic observations and/or reanalysis datasets are desirable.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

A High-Order Eulerian–Lagrangian Runge–Kutta Finite Volume (EL–RK–FV) Method for Scalar Nonlinear Conservation Laws

Abstract We present a class of high-order Eulerian–Lagrangian Runge–Kutta finite volume methods that can numerically solve Burgers’ equation with shock formations, which could be extended to general scalar conservation laws. Eulerian–Lagrangian (EL) and semi-Lagrangian (SL) methods have recently seen increased development and have become a staple for allowing large time-stepping sizes. Yet, maintaining relatively large time-stepping sizes post shock formation remains quite challenging. Our proposed scheme integrates the partial differential equation on a space-time region partitioned by linear approximations to the characteristics determined by the Rankine–Hugoniot jump condition. We trace the characteristics forward in time and present a merging procedure for the mesh cells to handle intersecting characteristics due to shocks. Following this partitioning, we write the equation in a time-differential form and evolve with Runge–Kutta methods in a method-of-lines fashion. High-resolution methods such as ENO and WENO-AO schemes are used for spatial reconstruction. Extension to higher dimensions is done via dimensional splitting. Numerical experiments demonstrate our scheme’s high-order accuracy and ability to sharply capture post-shock solutions with large time-stepping sizes.

Chen, Jiajie↗
DOE OSTI2025

Dataset for manuscript "Equipartition and the temperature of maximum density of TIP4P/2005 water"

We simulate TIP4P/2005 water in the temperature range of 257 K to 318 K with time-steps 0.25, 0.50, 1.00, 2.00, and 4.00 fs. The density-temperature behavior obtained using 0.25 or 0.50 fs are in excellent agreement with each other but differ from those obtained using time-steps that have been shown earlier to lead to a breakdown of equipartition. The temperature of maximum density (TMD) is 277.15 K with time-step 0.25 or 0.50 fs, but is shifted to progressively lower values for longer time-steps, a trend that holds for different thermostat/barostat combinations. Enhancing the water-water dispersion interaction, as has been recommended for simulating disordered proteins in TIP4P/2005, degrades the description of the liquid-vapor phase envelope. We present a simple physically transparent reasoning to highlight the separation of the time-scales between translational and rotational motion. We also develop a metric, Chi, that we term the equipartition anomaly, to detect equipartition violations in simulations that include molecules that are treated as rigid objects. Calculating Chi is shown to be straightforward and sensitive to equipartition violations. A key takeaway from this study is that using sufficiently short time-steps (less than or equal to 0.5 fs) to preserve equipartition is essential for obtaining meaningful liquid water properties and for producing reliable simulation data, as correct-ensemble sampling is fundamental to ensure reproducibility across codes and simulation alogrithms. The included dataset provides the raw data used in the preparation of the graphs noted in the manuscript.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Localized Exponential Time Differencing Method for Shallow Water Equations: Algorithms and Numerical Study

Here, we explore the performance of the exponential time differencing (ETD) method applied to the rotating shallow water equations. Comparing with explicit time stepping of the same order accuracy in time, the ETD algorithms could reduce the computational time in many cases by allowing the use of large time step sizes while still maintaining numerical stability. To accelerate the ETD simulations, we propose a localized approach that synthesizes the ETD method and overlapping domain decomposition. By dividing the original problem into many subdomain problems of smaller sizes and solving them locally, the proposed approach could speed up the calculation of matrix exponential vector products. Several standard test cases for shallow water equations of one or multiple layers are considered. The results show great potential of the localized ETD method for high-performance computing because each subdomain problem can be naturally solved in parallel at every time step.

58 GEOSCIENCES↗
DOE OSTI2026

Equipartition and the Temperature of Maximum Density of TIP4P/2005 Water

Here, we simulate TIP4P/2005 water in the temperature range of 257 to 318 K with time-steps δ = 0.25, 0.50, 1.00, 2.00, and 4.00 fs. The density–temperature behavior obtained using 0.25 or 0.50 fs is in excellent agreement with each other but differs from those obtained using time steps that have been shown earlier to lead to a breakdown of equipartition. For δt = 0.25 or 0.50 fs, the temperature of maximum density (TMD) is 277.15 K and the density value is in close agreement with experiments. For δt = 1.00 fs, the TMD is 277.15 K, but the density value is shifted higher. For the other time steps considered here, the TMD is shifted to progressively lower values for longer time steps, a trend that holds for different thermostat/barostat combinations. Enhancing the water–water dispersion interaction, as has been recommended for simulating disordered proteins in TIP4P/2005, degrades the description of the liquid–vapor phase envelope. We present a simple physically transparent explanation that highlights the separation of the time scales between translational and rotational motion. We also develop a metric, χ, that we term the equipartition anomaly, to detect equipartition violations in simulations that include molecules that are treated as rigid objects. Calculating χ is shown to be straightforward and sensitive to equipartition violations. A key takeaway from this study is that using sufficiently short time steps (≤0.5 fs) to preserve equipartition is essential for obtaining meaningful liquid water properties and for producing reliable simulation data, as correct ensemble sampling is fundamental to ensure reproducibility across codes and simulation algorithms.

Asthagiri, Dilipkumar N. [Oak Ridge National Labor↗
DOE OSTI2023

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗