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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

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↗
NASA NTRS1999

Acoustic Treatment Design Scaling Methods: Numerical Simulation of the Nonlinear Acoustic Impedance of a Perforated Plate Single-Degree-of-Freedom Resonator Using a Time-Domain Finite Difference Method - Volume 4

Single-degree-of-freedom resonators consisting of honeycomb cells covered by perforated facesheets are widely used as acoustic noise suppression liners in aircraft engine ducts. The acoustic resistance and mass reactance of such liners are known to vary with the intensity of the sound incident upon the panel. Since the pressure drop across a perforated liner facesheet increases quadratically with the flow velocity through the facesheet, this is known as the nonlinear resistance effect. In the past, two different empirical frequency domain models have been used to predict the Sound Pressure Level effect of the incident wave on the perforated liner impedance, one that uses the incident particle velocity in isolated narrowbands, and one that models the particle velocity as the overall velocity. In the absence of grazing flow, neither frequency domain model is entirely accurate in predicting the nonlinear effect that is measured for typical perforated sheets. The time domain model is developed in an attempt to understand and improve the model for the effect of spectral shape and amplitude of multi-frequency incident sound pressure on the liner impedance. A computer code for the time-domain finite difference model is developed and predictions using the models are compared to current frequency-domain models.

Kraft, R. E.↗
DOE OSTI2022

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↗
DOE OSTI2021

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↗
DOE OSTI2022

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↗
NASA NTRS1994

Navier-Stokes Solutions of Rotor and Rotor-Body Flows

This paper will review the advances made recently in the Navier-Stokes CFD methods to simulate aerodynamics and aeroacoustics of helicopter rotors and rotor-body flows. Although a complete flowfield simulation of full helicopter is currently not feasible with these methods, impressive gains have been made in analyzing individual components of this complex problem in a very detailed manner. The use of the state-of-the-art numerical algorithms in solution methods, in conjunction with powerful supercomputers, like the Cray-2, have enabled noticeable progress to be made in modeling viscous-inviscid interactions, blade-vortex interactions, tip-vortex: simulation and wake effects, as well as high speed impulsive noise in hover and forward flight for isolated rotor blades. This paper will critically evaluate the presently available Euler and Navier-Stokes methods, both finite-difference and finite volume methods using structured and unstructured grids for helicopter applications for accuracy, suitability, and computational efficiency. The review will also include the recent progress made using overset grids to model rotor-body flows. All the material for this review will be drawn from the published material shown below.

Srinivasan, G. R.↗
NASA NTRS2019

Weighted Least-Squares Cell-Average Gradient Construction Methods for the VULCAN-CFD Second-Order Accurate Unstructured-Grid Cell-Centered Finite-Volume Solver

The ability to solve the equations governing the hypersonic turbulent flow of a real gas on unstructured grids using a spatially-elliptic, 2nd-order accurate, cell-centered, finite-volume method has been recently implemented in the VULCAN-CFD code. The construction of cell-average gradients using a weighted linear least-squares method and the use of these gradients in the construction of the inviscid fluxes is the focus of this paper. A comparison of least-squares stencil construction methodologies is presented and approaches to augment the number of cells participating in the stencil while preserving accuracy are explored. Due to our interest in hypersonic flow, a robust multidimensional cell-average gradient limiter procedure that is consistent with the stencil used to construct the cell-average gradients is described and investigated. Canonical problems are computed to illustrate the challenges and investigate the accuracy, robustness and convergence behavior of the cell-average gradient methods on unstructured cell-centered finite-volume grids. Finally, thermally perfect, chemically frozen, Mach 8 turbulent flow of air around a blunt wedge is computed to demonstrate the robustness and convergence behavior of the new method for constructing stencils of use in a weighted linear least-squares gradient method for a hypersonic flow.

White, Jeffery A.↗
NASA NTRS1995

Development of methods for predicting large crack growth in elastic-plastic work-hardening materials in fully plastic conditions

The objects of the first, exploratory, stage of the project were listed as: (1) to make a detailed and critical review of the Boundary Element method as already published and with regard to elastic-plastic fracture mechanics, to assess its potential for handling present concepts in two-dimensional and three-dimensional cases. To this was subsequently added the Finite Volume method and certain aspects of the Finite Element method for comparative purposes; (2) to assess the further steps needed to apply the methods so far developed to the general field, covering a practical range of geometries, work hardening materials, and composites: to consider their application under higher temperature conditions; (3) to re-assess the present stage of development of the energy dissipation rate, crack tip opening angle and J-integral models in relation to the possibilities of producing a unified technology with the previous two items; and (4) to report on the feasibility and promise of this combined approach and, if appropriate, make recommendations for the second stage aimed at developing a generalized crack growth technology for its application to real-life problems.

Ford, Hugh↗
DOE OSTI2022

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↗
NASA NTRS2004

Three-Dimensional High-Order Spectral Volume Method for Solving Maxwell's Equations on Unstructured Grids

A three-dimensional, high-order, conservative, and efficient discontinuous spectral volume (SV) method for the solutions of Maxwell's equations on unstructured grids is presented. The concept of discontinuous 2nd high-order loca1 representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) method, but instead of using a Galerkin finite-element formulation, the SV method is based on a finite-volume approach to attain a simpler formulation. Conventional unstructured finite-volume methods require data reconstruction based on the least-squares formulation using neighboring cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In the SV method, one starts with a relatively coarse grid of triangles or tetrahedra, called spectral volumes (SVs), and partition each SV into a number of structured subcells, called control volumes (CVs), that support a polynomial expansion of a desired degree of precision. The unknowns are cell averages over CVs. If all the SVs are partitioned in a geometrically similar manner, the reconstruction becomes universal as a weighted sum of unknowns, and only a few universal coefficients need to be stored for the surface integrals over CV faces. Since the solution is discontinuous across the SV boundaries, a Riemann solver is thus necessary to maintain conservation. In the paper, multi-parameter and symmetric SV partitions, up to quartic for triangle and cubic for tetrahedron, are first presented. The corresponding weight coefficients for CV face integrals in terms of CV cell averages for each partition are analytically determined. These discretization formulas are then applied to the integral form of the Maxwell equations. All numerical procedures for outer boundary, material interface, zonal interface, and interior SV face are unified with a single characteristic formulation. The load balancing in a massive parallel computing environment is therefore easier to achieve. A parameter is introduced in the Riemann solver to control the strength of the smoothing term. Important aspects of the data structure and its effects to communication and the optimum use of cache memory are discussed. Results will be presented for plane TE and TM waves incident on a perfectly conducting cylinder for up to fifth order of accuracy, and a plane wave incident on a perfectly conducting sphere for up to fourth order of accuracy. Comparisons are made with exact solutions for these cases.

Liu, Yen↗
NASA NTRS1985

Multi-grid calculation of transonic potential flows

The finite-volume method discussed by Jameson and Caughey (1977), and Caughey and Jameson (1979, 1980) has made it possible to calculate the transonic potential flow past any configuration for which a suitable boundary-conforming coordinate grid can be constructed. However, computations for practical three-dimensional problems have remained quite expensive in terms of the required computer time. The reason for this is primarily related to the large number of grid cells necessary for adequate resolution in these complex three-dimensional problems, taking into account the large number of iterations required to achieve even modest convergence on these fine grids. The present chapter provides a description of work directed at removing this latter difficulty by making use of the multigrid method. Attention is given to finite-volume formulation, multigrid iteration, geometrical aspects, and computed results.

Caughey, D. A.↗
DOE OSTI2024

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↗
NASA NTRS1991

Development of iterative techniques for the solution of unsteady compressible viscous flows

Efficient iterative solution methods are being developed for the numerical solution of two- and three-dimensional compressible Navier-Stokes equations. Iterative time marching methods have several advantages over classical multi-step explicit time marching schemes, and non-iterative implicit time marching schemes. Iterative schemes have better stability characteristics than non-iterative explicit and implicit schemes. Thus, the extra work required by iterative schemes can also be designed to perform efficiently on current and future generation scalable, missively parallel machines. An obvious candidate for iteratively solving the system of coupled nonlinear algebraic equations arising in CFD applications is the Newton method. Newton's method was implemented in existing finite difference and finite volume methods. Depending on the complexity of the problem, the number of Newton iterations needed per step to solve the discretized system of equations can, however, vary dramatically from a few to several hundred. Another popular approach based on the classical conjugate gradient method, known as the GMRES (Generalized Minimum Residual) algorithm is investigated. The GMRES algorithm was used in the past by a number of researchers for solving steady viscous and inviscid flow problems with considerable success. Here, the suitability of this algorithm is investigated for solving the system of nonlinear equations that arise in unsteady Navier-Stokes solvers at each time step. Unlike the Newton method which attempts to drive the error in the solution at each and every node down to zero, the GMRES algorithm only seeks to minimize the L2 norm of the error. In the GMRES algorithm the changes in the flow properties from one time step to the next are assumed to be the sum of a set of orthogonal vectors. By choosing the number of vectors to a reasonably small value N (between 5 and 20) the work required for advancing the solution from one time step to the next may be kept to (N+1) times that of a noniterative scheme. Many of the operations required by the GMRES algorithm such as matrix-vector multiplies, matrix additions and subtractions can all be vectorized and parallelized efficiently.

Sankar, Lakshmi N.↗
NASA NTRS1988

Unsteady transonic airfoil computation using the integral solution of full-potential equation

The shock-capturing integral-equation scheme developed by Kandil and Hu (1987) for the analysis of steady transonic flow over airfoils is extended to the unsteady case. The full potential formulation of the governing equations is reviewed; the solution method is outlined; and results for a NACA 0012 airfoil in forced pitching oscillation at Mach 0.755 are presented in extensive graphs and briefly characterized. The present technique is shown to require significantly less computation time than finite-difference or finite-volume methods, and to give shock-motion predictions in good agreement with those of an implicit finite-volume Euler solver; the surface-pressure peaks are slightly underpredicted.

Kandil, O. A.↗
DOE OSTI2022

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↗
DOE OSTI2026

Numerical Investigation of Fluid Flow and Space Charge in Liquid Argon Time Projection Chamber (LArTPC) Detectors

Overview This project focused on developing a high-fidelity numerical framework to simulate the multiphysics environment within Liquid Argon Time Projection Chamber (LArTPC) detectors. The primary objective was to characterize the complex interplay between ion transport, background fluid dynamics, and electric field distortions—a critical factor for the calibration and sensitivity of next-generation High Energy Physics experiments, such as DUNE. Technical Achievements The research successfully yielded a hybrid numerical space-charge solver utilizing a Cell-Centered Finite Volume Method (FVM) for ion transport coupled with a Finite Element Method (FEM) for electric potential. Key accomplishments include: • Verification & Validation: The 3-D solver was rigorously verified against 1-D analytical solutions, demonstrating high numerical accuracy in predicting space-charge-induced field deviations. • Field Distortion Analysis: 3D simulations revealed that space charge effects introduce significant non-uniformities in the electric field. Critically, the research identified that background LAr flow velocities, when comparable to ion drift velocities, markedly exacerbate these distortions. • Technology Transfer: The resulting source code and comprehensive user manuals were successfully transferred to collaborators at Fermilab, providing a portable computational tool for the broader scientific community. Challenges and Future Directions While the space-charge solver achieved all performance metrics, the integrated fluid dynamics modeling encountered convergence challenges stemming from the extreme 200-fold disparity in length scales between the detector's 37 mm inlet pipes and the 8-meter global domain. To address this, the project has identified a clear technical pivot toward Hierarchical Geometric Adaptive Mesh Refinement (HG-AMR). By implementing an h-type refinement strategy with hanging nodes, future iterations of this solver will be capable of resolving localized high-gradient inlet flows without the prohibitive computational costs of regular grids. This advancement, combined with data-driven uncertainty quantification based on MicroBooNE-style calibration, will enable the precise modeling of detector responses in large-scale cryogenic environments where direct measurement remains difficult. Impact The computational tools developed under this award provide a foundation for enhancing the energy resolution and spatial reconstruction of noble liquid detectors. By bridging the gap between theoretical fluid dynamics and experimental field calibration, this work supports the DOE’s mission to advance the frontiers of neutrino physics and dark matter detection.

42 ENGINEERING↗
NASA NTRS2004

Discontinuous Spectral Difference Method for Conservation Laws on Unstructured Grids

A new, high-order, conservative, and efficient discontinuous spectral finite difference (SD) method for conservation laws on unstructured grids is developed. The concept of discontinuous and high-order local representations to achieve conservation and high accuracy is utilized in a manner similar to the Discontinuous Galerkin (DG) and the Spectral Volume (SV) methods, but while these methods are based on the integrated forms of the equations, the new method is based on the differential form to attain a simpler formulation and higher efficiency. Conventional unstructured finite-difference and finite-volume methods require data reconstruction based on the least-squares formulation using neighboring point or cell data. Since each unknown employs a different stencil, one must repeat the least-squares inversion for every point or cell at each time step, or to store the inversion coefficients. In a high-order, three-dimensional computation, the former would involve impractically large CPU time, while for the latter the memory requirement becomes prohibitive. In addition, the finite-difference method does not satisfy the integral conservation in general. By contrast, the DG and SV methods employ a local, universal reconstruction of a given order of accuracy in each cell in terms of internally defined conservative unknowns. Since the solution is discontinuous across cell boundaries, a Riemann solver is necessary to evaluate boundary flux terms and maintain conservation. In the DG method, a Galerkin finite-element method is employed to update the nodal unknowns within each cell. This requires the inversion of a mass matrix, and the use of quadratures of twice the order of accuracy of the reconstruction to evaluate the surface integrals and additional volume integrals for nonlinear flux functions. In the SV method, the integral conservation law is used to update volume averages over subcells defined by a geometrically similar partition of each grid cell. As the order of accuracy increases, the partitioning for 3D requires the introduction of a large number of parameters, whose optimization to achieve convergence becomes increasingly more difficult. Also, the number of interior facets required to subdivide non-planar faces, and the additional increase in the number of quadrature points for each facet, increases the computational cost greatly.

Liu, Yen↗
DOE OSTI2024

A Verification Suite of Test Cases for the Barotropic Solver of Ocean Models

Abstract The development of any atmosphere or ocean model warrants a suite of test cases (TCs) to verify its spatial and temporal discretizations, order of accuracy, stability, reproducibility, portability, scalability, etc. In this paper, we present a suite of shallow water TCs designed to verify the barotropic solver of atmosphere and ocean models. These include the non‐dispersive coastal Kelvin wave; the dispersive inertia‐gravity wave; the dispersive planetary and topographic Rossby waves; the barotropic tide; and a non‐linear manufactured solution. These TCs check the implementation of the linear pressure gradient term; the linear constant or variable‐coefficient Coriolis and bathymetry terms; and the non‐linear advection terms. Simulation results are presented for a variety of time‐stepping methods as well as two spatial discretizations: a mimetic finite volume method based on the TRiSK scheme, and a high‐order discontinuous Galerkin spectral element method. The experimental procedure for conducting these numerical experiments is detailed. It underscores several key considerations that vary depending on the chosen spatial discretization method. Finally, convergence studies of every TC are conducted with refinement in both space and time, only in space, and only in time. The convergence slopes match the expected theoretical predictions.

54 ENVIRONMENTAL SCIENCES↗