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NEAMS TH CRAB

The MOOSE framework is a library designed to make it straightforward for physicists and engineers to model partial differential equations using finite element and finite volume methods. Finite elements have been a part of the framework library since MOOSE's inception over a decade ago. Initial finite volume capability, however, was added only as recently as May of 2020. Since that time, significant work has been conducted to develop fluid modeling capability based on the finite volume method. Much of this work has taken place in MOOSE's navier_stokes module and in the NEAMS program's coarse mesh CFD code Pronghorn. We report here on development in MOOSE and Pronghorn of incompressible, porous incompressible, and weakly compressible finite volume simulation capabilities and their application to modeling of MSR and FHR advanced reactor concepts.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

High Fidelity CFD Simulations Supporting the KP-FHR

Kairos Power, LLC, is developing its version of the Fluoride-cooled High-temperature Reactor, the KP-FHR. The design uses a pebble bed core with fluoride salt as a coolant. The pebbles used in the KP-FHR have a diameter of 4 cm, with a shell fuel region where TRISO particles are embedded. A Pebble bed core design is adopted by several Gen IV reactors, They boast many benefits, such as fuel integrity, highly efficient heat transfer, and passive safety. However, it is challenging to accurately predict temperature and flow inside a pebble bed. Traditional approaches use the porous media model, which regards the pebble bed as a continuous medium, but with different temperature fields representing different levels, such as the fluid temperature, pebble surface temperature, and pebble center temperature. Empirical heat transfer correlations are adopted to calculate the heat transfer coefficient between different phases. However, empirical correlations are usually validated with experimental data, which usually lacks detail inside the pebble bed. The available experimental data is also generally at a high Reynolds number, which falls outside of the conditions of KP-FHR. Explicit computational fluid dynamics (CFD) simulations of randomly packed pebble beds have only become feasible recently. This is thanks to the rapid development of computational power and scalable algorithms. In this work, we used the Spectral Element Method (SEM) CFD code NekRS to simulate the randomly packed pebble bed in a cylindrical container. NekRS, which is the GPU variant of Nek5000, but refactored to utilize the computational power of GPUs using the OCCA library to run on hybrid architecture high performance computing systems. It was initially developed with the libParamunal library, but truncated and tuned for large-scale turbulence simulation. As a result, the SEM reaches higher precision with the same degrees of freedom by using a high-order Lagrange polynomial basis distributed on Gauss-Lobatto-Legendre quadrature inside each element, compared to lower-order methods, such the Finite Volume Method and Finite Element Method. The report is divided into five parts. We start with a general discussion of the pebble bed reactor, along with a specific investigation into the KP-FHR. The second part presents the numerical methodology. In the third part, we study a modular pebble bed with 1741 pebbles in a container of 7 pebble-diameter radius. Beyond LES simulations done by NekRS, we also leveraged the thermal radiation model in OpenFOAM to study heat transfer under no-forced-flow scenarios. Then, in the fourth part we simulated a pebble bed similar to the size of the Hermes Test Reactor. The total number of pebbles is in these simulations is 34,374. The container radius is 14 pebble-diameters. Finally, the report concludes in part five, with a discussion of future work.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

Large-eddy simulation of non-vaporizing sprays using the spectral-element method

Predictive simulations of high-pressure sprays require accurate representation of the turbulent gaseous flow field generated by liquid jet. Typically, the accuracy that can be obtained with low-order numerical methods (e.g. finite volume, finite element) is limited by stability issues in fine grids and the order of convergence of the method. In this work, we resolve the turbulent flow field in an Eulerian manner using the high-order spectral element method, coupled with a Lagrangian parcels approach to model the atomizing liquid jet. Large eddy simulations of single-hole sprays under non-evaporative conditions were conducted and compared against experimental data from Margot et al. (2008) and Spray A data from the Engine Combustion Network. The sensitivity of liquid penetration and droplet sizes to different breakup model parameters was studied. The effect of different numerical parameters, such as polynomial order of the solution (grid resolution), on liquid penetration was also analyzed. The method achieved grid-independent results using p-refinement, achieving finer resolution (by a factor of x 1.7 - x 3.5) in the gas-phase solution than in state-of-the-art simulations using the finite-volume method. Here the results showed good agreement with experimental data, demonstrating the ability of the current method to accurately capture liquid penetration and the shape of the spray.

97 MATHEMATICS AND COMPUTING↗

Advanced System Thermal Fluids Solver Development for SAM

This work summarizes a feasibility study on testing numerical algorithms that are suitable and efficient for advanced system analysis code development under the mutli-physics framework, MOOSE. The key is the implementation of a high-order one-dimensional staggered-grid finite volume method (SG-FVM), and its direct interaction with the linear/nonlinear solver, PETSc. Leveraging the existing capabilities of the SAM code, significant code coverages were established in the finite volume method code. This in turn allows for a suite of test problems with different problem sizes and levels of complexity to be used to quantify the performance improvement of the finite volume method code. As evidently shown in this study, the implemented SG-FVM demonstrated superior performance improvement against a direct finite element method implementation through MOOSE for the wide range of selected problems. On two computer systems, the speedup was observed to be significant, with at least one order of magnitude of solving time reduction. In addition, for a complex reactor model, transient simulation was performed using the finite volume method code, the results of which agree very well with the reference results from the finite element method code. Overall, this study demonstrates a successful feasibility study on the proposed numerical algorithms and software structure to support advanced system analysis tool development. In this work, short-term priority development and testing items were identified, and long-term code adoption and integration plans were made for the eventual deployment of the finite volume method in the SAM code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A fast matrix-free approach to the high-order control volume finite element method with application to low-Mach flow

Here, a fast matrix-free formulation of the control volume finite element method is presented, requiring much less memory and computational work than previous efforts. The method is implemented and evaluated as a solver for low-Mach flow, including the evaluation of a preconditioning strategy for the pressure Poisson equation. The efficiency and scaling with polynomial order is evaluated on simple turbulent flows of interest, with appropriate solution quality metrics, and compared with a reference node-centered finite volume discretization. For a turbulent channel flow test, we show improvement in computational work for a given accuracy with the high-order scheme. The performance on a GPU accelerated platform is also investigated, with benefit shown for the matrix-free discretization.

42 ENGINEERING↗

Improvement of Numerical Methods in Pronghorn

During the fiscal year of 2021, the finite-volume method (FVM) was deployed in Pronghorn to provide improved efficiency, stability, and accuracy for coarse-mesh, thermal-hydraulics problems. While the main goals of fiscal year 2021 were met, several issues emerged from the early deployment of the finite-volume method in Pronghorn. These issues were: The compressible and incompressible formulations that were implemented are inadequate for many nuclear reactor flow problems; Omission of terms accounting for the porosity and Darcy-Forchheimer body force discontinuities in the Rhie-Chow interpolation lead to oscillations in pressure and velocity at these discontinuities; The FVM lacks a correction for non-orthogonal grids for computing accurate pressure gradient leading to loss of accuracy in regions with skewed elements; The FVM currently uses a monolithic solver. Monolithic solvers have issues dealing with the saddle-point nature of the discretized fluid equations. The result are bad convergence if direct factorization is not used and large memory consumption when direct factorization is used. These four issues are addressed in this report. In particular, we report the completion of the following task: Implementation of a weakly compressible formulation in the MOOSE Navier-Stokes module; Implementation of Moukalled’s method for including body forces in the RCI. Additionally, we identified the need to smooth the porosity using Moukalled’s face-cell smoothing operator; Implementation of a non-orthogonal correction for the Green-Gauss gradient computation; Preliminary implementation of a SIMPLE segregated solver.

97 MATHEMATICS AND COMPUTING↗

A Block-Structured Adaptive Mesh Framework to Solve Radiation Transfer Equation in Irregular Embedded Geometries

Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.

computational fluid dynamics (CFD)↗

Investigation of Numerical Methods for Performance Improvement of MOOSE-based System Analysis Codes

The main objective of this study is to investigate the feasibility of implementation of staggered-grid finite volume method (SG-FVM) using the MOOSE framework to support the development of the advanced system analysis code SAM. This study successfully demonstrated the integration of staggered-grid finite volume method in the application level using the MOOSE framework, although not in the framework level which should be investigated in the future. Several important properties of the implemented SG-FVM, e.g., high-order spatial accuracy and monotonicity preserving, have been demonstrated with selected numerical test cases. The superior performance in execution time was also evident based on a selected one- dimensional flow problem in a loop configuration.

97 MATHEMATICS AND COMPUTING↗

Enhancing photoionization rate calculations in low-temperature plasmas using spectral methods

Photoionization plays a central role in the development of streamer discharges and other non-equilibrium plasma phenomena. It creates seed electrons, which are essential for positive streamer propagation, allowing the ionization front to move forward. Because of this, accurate modeling of photoionization is very important for predicting streamer behavior and plasma evolution. The photoionization process in air (N 2 – O 2 mixture) is often described by the Zheleznyak model (1982). This model is usually solved through Helmholtz-type equations that approximate the Zheleznyak photoionization model (Zheleznyak et al. 1982) as Partial Differential Equations (PDEs). Conventional numerical methods, such as the Finite Difference Method (FDM) or Finite Volume Method (FVM), are widely used to solve these equations. Although they are prevalent, the computational cost of these methods due to their need for matrix operations and iterative solver is demanding. To address this challenge, this work develops a spectral solver based on the Fast Fourier Transform (FFT) combined with Discrete Cosine Transform (DCT) and Discrete Sine Transform (DST) to calculate the photoionization rate efficiently in an axisymmetric cylindrical domain. This method naturally satisfies the boundary conditions used in the model and converts the PDE into algebraic ones in spectral space. Thus, avoids the need for iterative matrix solvers. When compared with FDM results, it is demonstrated that the new solver not only maintains accuracy, but also reduces the computational cost, showing a performance increase of approximately 100 compared to FDM over a wide range of problem sizes. The method is parallelized using Message Passing Interface (MPI) and has been integrated into a fluid plasma model for streamer simulation. Here, this FFT-based approach provides a fast and reliable alternative for calculating photoionization in fluid models, helping large-scale plasma simulations run faster and efficiently, and allows higher-resolution simulation without extra computational cost.

Axisymmetric system↗

Pronghorn Porous Media Model Validation with Pressure Drop Measurements

The verification and validation (V&V) of Pronghorn is imperative to assert its accuracy when predicting the fluid velocity, temperature, and pressure in high temperature gas-cooled reactors. Pronghorn is a coarse-mesh, intermediate-fidelity, and multidimensional thermal-hydraulics (TH) code developed by the Idaho National Laboratory (INL). New pebble bed experiments are used to observe the details of the fluid motion and pressure drop in the porous bed under the reactor normal operation. This paper focuses on the validation of the Pronghorn compressible and incompressible Navier-Stokes equations using the pressure drop measurements performed at the engineering-scale pebble bed facility at the Texas A&M university (TAMU). Various pressure drop correlations and porosity functions are implemented in both Pronghorn and STAR-CCM+ to compare the pressure drop due to the combined viscous and inertial resistances in the porous bed. The correlations accounting for the near-wall effect are also utilized to observe if the pressure drop estimates can be improved. Pronghorn porous media models predict the pressure drop well relative to the STAR-CCM+ simulation results and 1D correlations, and both the finite element method (FEM) and finite volume method (FVM) perform accurately. Pronghorn models are also validated with the experimental measurements given the different Reynolds number ranges and specific aspect ratios. The likelihood of the statistical significance between the pressure drop measurements and specific correlations or simulations is low provided that the overlap of their confidence intervals is more than the half of a single arm. Several validation metrics are reasonable in regard to the similar studies from other literature. The precise average pebble bed porosity estimation has much impact on the pressure drop, and the Foumeny and Montillet (dense packing) models carry out the accurate pressure drop prediction by considering the near-wall effect.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Meta Biome: a multiscale model integrating agent-based and metabolic networks to reveal spatial regulation in gut mucosal microbial communities

ABSTRACT Mucosal microbial communities (MMCs) are complex ecosystems near the mucosal layers of the gut essential for maintaining health and modulating disease states. Despite advances in high-throughput omics technologies, current methodologies struggle to capture the dynamic metabolic interactions and spatiotemporal variations within MMCs. In this work, we presentMetaBiome, a multiscale model integrating agent-based modeling (ABM), finite volume methods, and constraint-based models to explore the metabolic interactions within these communities. Integrating ABM allows for the detailed representation of individual microbial agents each governed by rules that dictate cell growth, division, and interactions with their surroundings. Through a layered approach—encompassing microenvironmental conditions, agent information, and metabolic pathways—we simulated different communities to showcase the potential of the model. Using ourin-silicoplatform, we explored the dynamics and spatiotemporal patterns of MMCs in the proximal small intestine and the cecum, simulating the physiological conditions of the two gut regions. Our findings revealed how specific microbes adapt their metabolic processes based on substrate availability and local environmental conditions, shedding light on spatial metabolite regulation and informing targeted therapies for localized gut diseases.MetaBiome provides a detailed representation of microbial agents and their interactions, surpassing the limitations of traditional grid-based systems. This work marks a significant advancement in microbial ecology, as it offers new insights into predicting and analyzing microbial communities. IMPORTANCE Our study presents a novel multiscale model that combines agent-based modeling, finite volume methods, and genome-scale metabolic models to simulate the complex dynamics of mucosal microbial communities in the gut. This integrated approach allows us to capture spatial and temporal variations in microbial interactions and metabolism that are difficult to study experimentally. Key findings from our model include the following: (i) prediction of metabolic cross-feeding and spatial organization in multi-species communities, (ii) insights into how oxygen gradients and nutrient availability shape community composition in different gut regions, and (iii) identification of spatiallyregulated metabolic pathways and enzymes inE. coli. We believe this work represents a significant advance in computational modeling of microbial communities and provides new insights into the spatial regulation of gut microbiome metabolism. The multiscale modeling approach we have developed could be broadly applicable for studying other complex microbial ecosystems.

Microbiology↗

Design of a Combined Proportional Integral Derivative Controller to Regulate the Temperature Inside a High-Temperature Tubular Solar Reactor

Solar fuels are proven to be promising candidates for thermochemical energy storage. However, the transient nature of solar radiation is an obstacle to maintaining a stable operational temperature inside a solar reactor. To overcome this challenge, the temperature of a solar reactor can be regulated by controlling the incoming solar radiation or the feedstock flowrate inside the reactor. In this work, a combined proportional integral derivative (PID) controller is implemented to regulate the temperature inside a high-temperature tubular solar reactor with counter-current flowing gas/particles. The control model incorporates two control systems to regulate incoming solar radiation and gas flow simultaneously. The design of the controller is based on a reduced-order numerical model of a high-temperature tubular solar reactor that is vertically oriented with an upward gas flow and downward particle flow. The reactor receives heat circumferentially through its wall over a finite segment of its length. Formulation of the heat transfer model is presented by applying the energy balance for the reactor tube and considering heat and mass transfer inside. A set of governing differential equations are solved numerically by using the finite volume method to obtain reactor wall, particles, and gas temperatures along the reactor length with various boundary conditions. Simulation results are used to tune the PID controller parameters by utilizing the Ziegler–Nichols tuning method. Both the simulation results and the controller performance are visualized on the LABVIEW platform. The controller is challenged to track different temperature setpoints with different scenarios of transient solar radiation. Here, the performance of the PID controller was compared to experimental results obtained from an industrial PID controller embedded in a 7 kW electric furnace. Results show that the combined PID controller is successful in maintaining a stable temperature inside the reactor by regulating the incoming solar radiation and the flowrate via small steady-state error and reasonable settling time and overshoot.

14 SOLAR ENERGY↗

Exponential Time Differencing Schemes for Fuel Depletion and Transport in Molten Salt Reactors: Theory and Implementation

A numerical framework for modeling depletion and mass transport in liquid-fueled molten salt reactions is presented based on exponential time differencing. The solution method involves using the finite volume method to transform the system of partial differential equations (PDEs) into a much larger system of ordinary differential equations. The key part of this method involves solving for the exponential of a matrix. We explore six different algorithms to compute the exponential in a series of progression problems that explore physical transport phenomena in molten salt reactors. This framework shows good results for solving linear parabolic PDEs with each of the six matrix exponential algorithms. For large problems, the series solvers such as Padé and Taylor have large run times, which can be mitigated by using the Krylov subspace.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

Development of a Subchannel Capability for Liquid-Metal Fast Reactors in Pronghorn

This report details the development and demonstration of an entirely new capability in Pronghorn, namely the ability to model liquid-metal fast reactor (LMFR) flow conditions on the engineering scale. We developed two modeling approaches for LMFR that can be used separately or be combined into a hybrid simulation: (1) a modern subchannel capability called Pronghorn-Subchannel for square and hexagonal lattices, and (2) a porous flow capability for LMFR geometries. The report emphasizes the novel aspects of the developed subchannel capability and the interoperability of the subchannel capability, porous flow capability, and multiphysics tools within the multiphysics object oriented simulation environment (MOOSE). Here we demonstrate the ability to: (1) Accurately model subchannel flow in hexagonal lattices; (2) Couple the subchannel flow model to multidimensional finite-element method (FEM) or finite-volume method (FVM) heat conduction models; (3) Model LMFRs using Pronghorn’s porous media FVM approach; (4) Couple porous flow FVM and subchannel models in a single simulation; (5) Explicitly model inter-wrapper flows along with conjugate heat transfer from the intra-element flow; and (6) Demonstrate the numerical robustness of the subchannel algorithm by simulating intra-element flow recirculation in a high-buoyancy, low-flow fuel element.

97 MATHEMATICS AND COMPUTING↗

First implementation of gyrokinetic exact linearized Landau collision operator and comparison with models

Gyrokinetic simulations are fundamental to understanding and predicting turbulent transport in magnetically confined fusion plasmas. Previous simulations have used model collision operators with approximate field-particle terms of unknown accuracy and/or have neglected collisional finite Larmor radius (FLR) effects. We have implemented the linearized Fokker–Planck collision operator with exact field-particle terms and full FLR effects in a gyrokinetic code (GENE). The new operator, referred to as “exact” in this paper, allows the accuracy of model collision operators to be assessed. The conservative Landau form is implemented because its symmetry underlies the conservation laws and the H-theorem, and enables numerical methods to preserve this conservation, independent of resolution. The implementation utilizes the finite-volume method recently employed to discretize the Sugama collision model in GENE, allowing direct comparison between the two operators. Results show that the Sugama model appears accurate for the growth rates of trapped electron modes (TEMs) driven only by density gradients, but appreciably underestimates the growth rates as the collisionality and electron temperature gradient increase. The TEM turbulent fluxes near the nonlinear threshold using the exact operator are similar to the Sugama model for the n e = d ln T e /d ln n e = 0 case, but substantially larger than the Sugama model for the n e = 1 case. The FLR effects reduce the growth rates increasingly with wavenumber deepening a “valley” at the intermediate binormal wavenumber as the unstable mode extends from the TEM regime to the electron temperature gradient instability regime. Application to the Hinton–Rosenbluth problem shows that zonal flows decay faster as the radial wavenumber increases and the exact operator yields weaker decay rates.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Adaptive clipping‐and‐redistribution algorithms for bounded and conservative high‐order interpolations applied to discontinuous and reactive flows

Abstract A new adaptive clipping‐and‐redistribution method is presented which provides bounds‐preservation for multidimensional interpolation in the context of high‐order finite‐volume discretizations with adaptive mesh refinement (AMR). The underlying finite‐volume method (FVM) for the computational fluid dynamics applications is fourth‐order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High‐order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high‐order interpolation method. First, the method needs to be bound‐preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth‐order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock‐induced ‐ combustion and a ‐air flame in a practical bluff‐body combustor. Results show the method prevents new extrema near discontinuities while maintaining high‐order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

97 MATHEMATICS AND COMPUTING↗

Robust 3D multi-material hydrodynamics using discontinuous Galerkin methods

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material (m ≥ 2) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

97 MATHEMATICS AND COMPUTING↗

Modelling the Lyman-α forest with Eulerian and SPH hydrodynamical methods

ABSTRACT We compare two state-of-the-art numerical codes to study the overall accuracy in modelling the intergalactic medium and reproducing Lyman-α forest observables for DESI and high-resolution data sets. The codes employ different approaches to solving both gravity and modelling the gas hydrodynamics. The first code, Nyx, solves the Poisson equation using the Particle-Mesh (PM) method and the Euler equations using a finite-volume method. The second code, CRK-HACC , uses a Tree-PM method to solve for gravity, and an improved Lagrangian smoothed particle hydrodynamics (SPH) technique, where fluid elements are modelled with particles, to treat the intergalactic gas. We compare the convergence behaviour of the codes in flux statistics as well as the degree to which the codes agree in the converged limit. We find good agreement overall with differences being less than observational uncertainties, and a particularly notable ≲1 per cent agreement in the 1D flux power spectrum. This agreement was achieved by applying a tessellation methodology for reconstructing the density in CRK-HACC instead of using an SPH kernel as is standard practice. We show that use of the SPH kernel can lead to significant and unnecessary biases in flux statistics; this is especially prominent at high redshifts, z ∼ 5, as the Lyman-α forest mostly comes from lower-density regions that are intrinsically poorly sampled by SPH particles.

79 ASTRONOMY AND ASTROPHYSICS↗