| 1. Domain | 1.1 Scope of the Domain | Boundaries | The range of phenomena the science includes and excludes. | Includes numerical simulation of fluid and plasma systems using discretized forms of governing equations; covers fluid dynamics, MHD, kinetic plasma models, turbulence modeling, multi scale coupling, wave propagation, reconnection, shocks, transport, and stability. Excludes purely analytical theory, experiments without computational components, and solid-state or materials simulations unless directly related to fluid or plasma behavior. |
| | Scale | The spatial, temporal, or organizational level at which the science operates (e.g., quantum, cellular, social, cosmic). | Operates from microscopic kinetic scales requiring fine resolution to macroscopic global systems such as reactors, atmospheres, magnetospheres, and astrophysical plasmas. Time scales range from microsecond wave dynamics to long-time evolution of global flows. |
| 1.2 Ontological Commitments | Entities | The kinds of things assumed to exist within the domain (particles, organisms, agents, fields, etc.). | Numerical grid cells, particles (in particle methods), field variables, boundary conditions, turbulence structures, waves, shocks, reconnection sites, and discretized representations of fluids or plasmas. |
| | Properties | The fundamental attributes these entities possess (mass, charge, genotype, preference, etc.). | Density, velocity, temperature, pressure, electric and magnetic fields, distribution functions, numerical fluxes, stability properties, error levels, and convergence behavior. |
| | Categories | The basic ontological types used to classify domain elements (substances, processes, relations, structures). | Fluid models, kinetic models, hybrid models, grid types, solver classes, turbulence closures, boundary conditions, physical modules, and numerical schemes. |
| 1.3 State-Variables | Variables | The measurable or definable properties that describe system conditions. | Density, velocity components, pressure, temperature, magnetic field, electric field, distribution function values, vorticity, current density, and auxiliary numerical variables such as residuals or timestep values. |
| | Parameterization | How variables encode and represent the system’s state. | States encoded through mesh resolution, timestep size, numerical dissipation coefficients, solver parameters, physical nondimensional numbers, initial conditions, and boundary conditions. |
| 1.4 Admissible Idealizations | Simplifications | Conceptual reductions used to make the domain tractable (point masses, rational agents, perfect gases). | Reduced dimensionality, symmetry assumptions, ideal MHD limits, incompressible flow assumptions, linearized equations, simplified collision operators, approximate turbulence closures, and coarse grid approximations. |
| | Validity Conditions | The limits and contexts in which idealizations hold or break down. | Valid when numerical resolution captures relevant physical scales, simplifications do not remove dominant physics, turbulence models remain stable, and kinetic effects are properly represented or negligible. Breaks down when resolution is insufficient or omitted physics becomes dominant. |
| 1.5 Domain Assumptions | Structural Assumptions | Background ontological stances such as determinism, continuity, randomness, discreteness. | Assumes governing equations accurately describe the physical system, numerical discretization faithfully approximates those equations, boundary conditions represent real constraints, and convergence indicates correctness. |
| | Implicit Commitments | Unstated but necessary assumptions that shape the field’s conceptual structure. | Assumes numerical stability reflects physical stability, discretization errors remain bounded, turbulence closures remain valid outside calibration regimes, and algorithmic approximations map meaningfully to real physical behavior. |
| 1.6 Internal Coherence Requirements | Consistency | The demand that domain concepts do not contradict one another. | Requires compatibility among equations, numerical schemes, boundary conditions, mesh structure, and solver stability; no contradictions between physical assumptions and discretization choices. |
| | Compatibility | The requirement that entities, variables, and assumptions fit together into a unified descriptive framework. | Entities, variables, and assumptions must together form a unified framework linking physical equations, numerical methods, solver algorithms, mesh resolution, and model closures into a coherent simulation environment. |
| 2. Evidence Layer | 2.1 Observable Phenomena | Observables | The aspects of the domain that can produce detectable signals accessible to measurement. | Observable outputs include velocity fields, pressure fields, density fields, temperature distributions, magnetic field evolution, electric field evolution, vorticity structures, shocks, waves, turbulence spectra, transport fluxes, and particle distribution functions in kinetic simulations. |
| | Detection Limits | The boundaries of what can be resolved or sensed by current instruments or methods. | Limited by numerical resolution, timestep stability, discretization error, mesh quality, solver precision, turbulence model accuracy, and inability to resolve kinetic or subgrid scales with coarse grids. |
| 2.2 Measurement Systems | Units | Standardized quantifications (meters, seconds, volts, decibels, dollars, etc.) necessary for consistent comparison. | Uses meters, seconds, pascals, teslas, volts per meter, density units, kelvins, electron volts, nondimensional units (Reynolds number, Mach number, plasma beta), and code-dependent normalized units. |
| | Instruments | Devices and tools (microscopes, spectrometers, sensors, surveys, detectors) used to produce measurements. | Instruments are numerical: solvers, mesh generators, diagnostics routines, visualization tools, particle trackers, field analyzers, turbulence diagnostics, shock finders, and error estimators. |
| 2.3 Operational Definitions | Definitions | Terms defined by specific measurement procedures, ensuring empirical clarity. | Terms such as residual, convergence threshold, Courant number, diffusion coefficient, flux, timestep stability limit, turbulence intensity, and energy spectrum are defined through the simulation’s numerical procedures. |
| | Procedures | The explicit steps required to perform a measurement in a reproducible way. | Procedures include mesh refinement, timestep adjustment, solver iteration, field interpolation, flux reconstruction, particle push algorithms, data filtering, and extraction of diagnostics like spectra or correlation functions. |
| 2.4 Data Acquisition | Protocols | Formal processes for gathering data under controlled or standardized conditions. | Data produced through periodic simulation outputs, checkpointing, high cadence dumps for turbulence or shocks, adaptive sampling in critical regions, and synchronized recording of solver and physical variables. |
| | Sampling | Rules determining which subset of the domain is measured and how representative it is. | Sampling rules include uniform or adaptive grid sampling, time sampling based on physics timescales, particle sampling in kinetic codes, and multi resolution sampling for multi scale coupling. |
| 2.5 Data Character & Format | Data Types | The form raw evidence takes (time series, spectra, images, counts, qualitative records). | Data appears as field arrays, particle lists, time series, spectra, correlation functions, error fields, mesh data, solver logs, and derived diagnostic products such as vorticity or current density. |
| | Resolution | The granularity or precision with which data is captured. | Determined by mesh size, particle count, solver accuracy, timestep constraints, computational limits, and numerical noise thresholds. |
| 2.6 Reliability & Calibration | Calibration | Adjustment procedures ensuring instruments produce accurate results. | Calibration uses convergence tests, mesh refinement studies, benchmark problems, analytic solution comparisons, verification suites, unit tests for solvers, and cross code validation. |
| | Error Characterization | Identification and quantification of noise, uncertainty, bias, and measurement error. | Errors arise from discretization, numerical diffusion, aliasing, inadequate resolution, solver instability, floating point error, subgrid model inaccuracies, and divergence between numerical and physical boundary conditions. |
| 3. Structural Layer | 3.1 Patterns & Regularities | Laws / Relations | Stable, repeatable patterns governing how observables behave across conditions. | Stable patterns include conservation of mass, momentum, energy, and magnetic flux (in appropriate models), predictable turbulence spectra, shock formation rules, wave dispersion relations, scaling relations across mesh resolution, and convergence patterns for stable numerical schemes. |
| | Invariants | Quantities or properties that remain constant under transformations (symmetries, conservation laws). | Invariants include discrete conservation of mass or energy in conservative schemes, magnetic flux preservation in constrained transport methods, stable nondimensional similarity relationships, and invariants encoded in symplectic or structure preserving integrators. |
| 3.2 Causal Architecture | Mechanisms | Underlying processes or structures that produce the observed regularities. | Mechanisms arise from discretized versions of advection, diffusion, Lorentz forces, reconnection, shock compression, wave propagation, numerical dissipation, and turbulence generation through nonlinear interactions across simulated scales. |
| | Pathways | Organized sequences of interactions forming a causal chain or network. | Pathways include cascading of turbulent energy from resolved to subgrid scales, development of numerical or physical instabilities, formation of shocks or discontinuities, magnetic field amplification through flow shear, and evolution of particle distribution functions in kinetic codes. |
| 3.3 Theoretical Vocabulary | Concepts | Core terms that encode the domain’s structure (force, gene, equilibrium, field). | Core terms include solver stability, convergence, timestep constraints, Courant number, flux limiter, turbulence closure, magnetic divergence control, numerical dissipation, subgrid model, particle pusher, and boundary scheme. |
| | Classifications | Taxonomies, categories, or typologies that organize entities and relations. | Classifies simulations by method (finite difference, finite volume, finite element, spectral, particle in cell, hybrid), by regime (fluid, MHD, kinetic), by geometry (2D, 3D, axisymmetric), and by application (turbulence, shocks, reconnection, waves). |
| 3.4 Formal Representations | Equations | Mathematical constructs expressing laws, relations, or mechanisms. | Includes discretized forms of Navier-Stokes equations, MHD equations, Maxwell’s equations, Vlasov equation, particle motion equations, turbulence closure equations, and numerical update rules such as Runge-Kutta or implicit solvers. |
| | Models | Structured representations—mathematical, computational, or conceptual—used to predict and explain phenomena. | Uses fluid solvers, MHD solvers, gyrokinetic models, particle in cell models, hybrid fluid kinetic models, turbulence models, shock capturing schemes, and multi physics coupling frameworks. |
| 3.5 Idealized Structures | Simplified Models | Purposeful abstractions that capture essential dynamics while omitting irrelevant detail. | Idealizations include reduced dimensionality, uniform grids, simplified boundary conditions, ideal MHD limits, linearized systems, coarse resolution approximations, and minimalistic collision operators. |
| | Limit Conditions | Regimes where specific models or approximations hold (classical vs. quantum, linear vs. nonlinear). | Valid when resolution exceeds physical scale requirements, numerical diffusion is small relative to physical diffusion, timestep satisfies stability conditions, and fluid or kinetic models accurately represent the governing physics; breaks down when mesh is too coarse or physics is omitted. |
| 3.6 Integrative Frameworks | Unifying Theories | Higher-order structures that connect disparate laws or mechanisms under a coherent whole. | Includes frameworks unifying discrete conservation, turbulence transport, wave propagation, reconnection physics, and kinetic or fluid scale behavior in a coherent numerical environment. |
| | Interdisciplinary Links | Points where the theory connects to adjacent sciences or larger explanatory systems. | Links to computational physics, applied mathematics, plasma physics, fluid dynamics, astrophysics, fusion research, computer science (parallel computing), and numerical analysis. |
| 4. Method Layer | 4.1 Inquiry Design | Experimental Design | Structured plans for manipulating variables to test causal claims. | Experiments involve adjusting mesh resolution, timestep size, solver type, numerical dissipation level, boundary condition configuration, physics modules, and perturbations to test causal effects on stability, turbulence, reconnection, shock behavior, or transport. Simulations act as controlled experiments on numerical representations of fluids or plasmas. |
| | Observational Design | Systematic approaches for gathering non-manipulated data (surveys, field studies, natural experiments). | Observational design uses natural numerical evolution without artificial perturbations, monitoring spontaneous development of instabilities, turbulence cascades, waves, or reconnection inside simulations initialized with physically motivated conditions. |
| 4.2 Testing & Validation | Hypothesis Testing | Procedures for evaluating whether evidence supports or contradicts specific claims. | Hypotheses tested by comparing numerical outcomes such as wave dispersion, instability growth rates, shock structure, turbulence spectra, or transport coefficients against analytic theory, benchmark experiments, or higher fidelity models. |
| | Replication | The requirement that results be independently reproducible under similar conditions. | Replication occurs by re running simulations with different solvers, independent codes, varied mesh structures, altered initial conditions, or alternative numerical methods to verify consistency of the results. |
| 4.3 Inference & Evaluation | Statistical Inference | Rules for drawing conclusions from noisy or incomplete data. | Statistical tools include spectral analysis, convergence studies, uncertainty quantification, ensemble averaging across multiple simulation runs, error estimation for numerical stability, and statistical evaluation of turbulence or transport metrics. |
| | Model Comparison | Criteria (fit, simplicity, predictive accuracy, robustness) used to evaluate competing models. | Models compared based on convergence behavior, accuracy relative to known analytic solutions, predictive ability for turbulence or instability behavior, computational efficiency, robustness across parameter ranges, and agreement with experimental or observational data. |
| 4.4 Error Management | Error Analysis | Identification and quantification of random and systematic errors. | Errors arise from discretization issues, mesh deformation, aliasing, floating point precision, timestep instability, numerical diffusion, inaccurate boundary schemes, subgrid model uncertainty, and solver divergence during nonlinear evolution. |
| | Bias Control | Methods for minimizing subjective, instrumental, or procedural biases. | Bias minimized by independent code verification, blind comparisons of solver outputs, standardized benchmark suites, controlled numerical experiments, mesh refinement studies, and cross checking results with alternate physics closures. |
| 4.5 Adjudication & Revision | Peer Scrutiny | Collective evaluation of claims through critique, review, and debate. | Findings evaluated through multi code comparison projects, validation against laboratory or space plasma data, peer review, replication in independent computational groups, and participation in international verification and validation campaigns. |
| | Theory Revision | Procedures for modifying, replacing, or discarding models based on new evidence. | Numerical theory revised when simulations reveal unphysical behavior, unexpected instabilities, anomalous transport scaling, or discrepancies with experiments, requiring improved closures, discretization methods, or turbulence models. |
| 4.6 Integrity Conditions | Transparency | Requirements to disclose methods, data, assumptions, and limitations. | Requires full disclosure of solver algorithms, mesh structure, timestep constraints, boundary conditions, numerical stability criteria, convergence tests, physical assumptions, and uncertainty estimates. |
| | Ethical Standards | Norms ensuring responsible conduct in experimentation, data handling, and publication. | Requires accurate reporting of numerical limitations, avoidance of selective result presentation, reproducibility of simulation setups, clear documentation of models and parameters, and adherence to best practices in computational science. |