Loci-Stream: Parallel Scalable Compressible Pressure-Based Solver Theory Guide

In addition to the derivation-focused theory chapters, this guide includes a separate Coding Guide chapter that summarizes the main solver data structures, assembly naming patterns, and math-to-code correspondences used throughout the implementation.

• 1. Governing Equations, Algorithm & Programming Framework
  • 1.1. Introduction
  • 1.2. Notation Conventions
  • 1.3. Instantaneous Governing Equations
  • 1.4. Governing Equations for Modeling Turbulent Flows
  • 1.5. The Loci RULE-BASED PROGRAMMING FRAMEWORK
  • 1.6. References
• 2. The Solution Algorithm
  • 2.1. Pressure-Based Algorithms for All-Speed Flows
  • 2.2. High-Level Solution Flow
  • 2.3. Notation Used In This Chapter
  • 2.4. SIMPLE-Family Pressure-Correction Form
  • 2.5. Algorithm Families
  • 2.6. References
• 3. Finite-Volume Transport and Pressure-Correction Assembly on Unstructured Grids
  • 3.1. Implemented Equation Snapshots
  • 3.2. From Transport Equations to Algebraic Rows
  • 3.3. From Continuity Defect to Pressure-Correction Row
  • 3.4. Applying the Pressure Correction
  • 3.5. Boundary Conditions
  • 3.6. References
• 4. High-Resolution Schemes for Compressible Flows
  • 4.1. AUSM±up for Unstructured Grids
  • 4.2. Simple Low-Dissipation AUSM (SLAU) Scheme
  • 4.3. SLAU/SLAU2 Momentum Equation
  • 4.4. SLAU/SLAU2 Pressure Correction Equation
  • 4.5. Standard Limiters: Barth-Jespersen (BJ) and Venkatakrishnan (V)
  • 4.6. Multidimensional Limiters
  • 4.7. Hybrid SLAU/SLAU2 Backends (van Leer, HLLE, HLLEM, LM-HLLEM, HLLEMCC)
• 5. Higher-Order Temporal Integration and Splitting
  • 5.1. Semi-Discrete Starting Point
  • 5.2. Crank-Nicolson: One-Step Second-Order Time Integration
  • 5.3. Second-Order Backward Differencing (BDF2)
  • 5.4. Source Splitting versus Unsplit Treatment
  • 5.5. Second-Order Strang Splitting for Reacting Flows
  • 5.6. References
• 6. Detailed Governing Equation Forms
  • 6.1. Common Definitions
  • 6.2. Generic Source-Term Notation
  • 6.3. Continuity Equation
  • 6.4. Momentum Equation
  • 6.5. Total Enthalpy Equation
  • 6.6. Total Energy Equation
  • 6.7. Temperature Equation
  • 6.8. Species Equation
  • 6.9. Solver-Form Notes
  • 6.10. Summary
  • 6.11. References
• 7. Non-Inertial Reference-Frame Formulation
  • 7.1. Reference-Frame Definitions
  • 7.2. Velocity Relation Between Inertial And Non-Inertial Frames
  • 7.3. Apparent Acceleration In The Moving Frame
  • 7.4. Momentum Equation In The Non-Inertial Frame
  • 7.5. Code-Facing Form Used In Loci-Stream
  • 7.6. Where Else The Same Terms Enter
  • 7.7. Implementation Notes For The Reference-Frame Data
• 8. Additive-Volume Real-Fluid EOS Closure
  • 8.1. Notation
  • 8.2. EOS Call Inputs and Work Arrays
  • 8.3. Additive-Volume Mixture Rule
  • 8.4. Mixture Energy and Enthalpy
  • 8.5. The (p,T,Y) Query
  • 8.6. The (p,\rho,Y) Query
  • 8.7. The (p,h,Y) Query
  • 8.8. Face Reconstruction Guidance
  • 8.9. Implementation Map
• 9. Double-Flux Method for a Pressure-Based Segregated Solver
  • 9.1. Source of Pressure Oscillations
  • 9.2. Contact-Interface Balance
  • 9.3. Density-Based Double-Flux Form
  • 9.4. Cellwise Freezing and Quasi-Conservation
  • 9.5. Translation to a Pressure-Based Solver
  • 9.6. Energy and Enthalpy Forms
  • 9.7. Pressure-Correction Density Response
  • 9.8. Face Fluxes in the Pressure-Based Form
  • 9.9. Assumptions and Limits
  • 9.10. Hybrid Conservative / Double-Flux Strategies
  • 9.11. Summary
  • 9.12. References
• 10. Geometric Conservation Law for Moving Meshes
  • 10.1. Introduction
  • 10.2. Overview
  • 10.3. ALE Form and the Geometric Conservation Law
  • 10.4. Discrete GCL Statement
  • 10.5. Face-Based GCL: Facet Decomposition and Time-Averaged Area Vectors
  • 10.6. How This Appears in src/movingMesh.loci
  • 10.7. Assumptions and Limitations
  • 10.8. References
• 11. Nonreflecting Open Boundary Conditions
  • 11.1. Characteristic Background
  • 11.2. Notation
  • 11.3. Boundary-State Philosophy
  • 11.4. Inlet Formulation
  • 11.5. Outlet Formulation
  • 11.6. Interpretation of the Relaxation Parameters
  • 11.7. Closing Remarks
  • 11.8. Literature Context
• 12. Classical Cartesian Pressure-Correction Derivation
  • 12.1. The SIMPLE algorithm on non-staggered grids
  • 12.2. The SIMPLEC algorithm
  • 12.3. References
• 13. Pressure-Correction Equation Forms
  • 13.1. Reference Equation Form
  • 13.2. Common Algebraic Backbone
  • 13.3. The Face-Coefficient Pipeline
  • 13.4. Form Families
  • 13.5. Additional Compressible Density-Correction Term at Faces
  • 13.6. Species-Summed Volumetric Form
  • 13.7. Code Mapping Summary
• 14. Density-Pressure Linearization In Pressure Correction
• 15. How Does Continuity Know The Provisional Velocity Is Incorrect?
• 16. Solver Framework Reference
  • 16.1. 1  Solver
  • 16.2. 2  Mesh & connectivity cheat‑sheet
  • 16.3. 2.5 Math-to-Code Naming Map
  • 16.4. 3  Momentum block (velocity predictor)
  • 16.5. 4  Pressure‑correction block
  • 16.6. 5 Life‑cycle of the pPrime variables
  • 16.7. 7 Reference equations

Indices and tables

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