Nalu-Wind - Theory Manual

Nalu-Wind represents a generalized unstructured, massively parallel, variable density turbulent flow capability designed for energy applications. This code base began as an effort to prototype Sierra Toolkit, [EWS+10], usage along with direct parallel matrix assembly to the Trilinos, [HBH+03], Epetra and Tpetra data structure. However, the simulation tool has evolved as a tool to support a variety of research projects germane to the energy sector including wind aerodynamic prediction and traditional gas-phase combustion applications.

• 1. Low Mach Number Derivation
  • 1.1. Asymptotic Expansion
• 2. Supported Equation Set
  • 2.1. Conservation of Mass
  • 2.2. Conservation of Momentum
  • 2.3. Filtered Mixture Fraction
  • 2.4. Conservation of Energy
  • 2.5. Review of Prandtl, Schmidt and Unity Lewis Number
  • 2.6. Thermal Heat Conduction
  • 2.7. ABL Forcing Source Terms
  • 2.8. Conservation of Species
  • 2.9. Subgrid-Scale Kinetic Energy One-Equation LES Model
  • 2.10. RANS Model Suite
  • 2.11. Laminar-Turbulent Transition Model Formulation
  • 2.12. Detached Eddy Simulation (DES) Formulation
  • 2.13. Active Model Split (AMS) Formulation
  • 2.14. Solid Stress
  • 2.15. Moving Mesh
  • 2.16. Radiative Transport Equation
  • 2.17. Wall Distance Computation
• 3. Discretization Approach
  • 3.1. CVFEM Dual Mesh
  • 3.2. Edge-Based Discretization
  • 3.3. Projected Nodal Gradients
  • 3.4. Time and Source Terms
  • 3.5. Diffusion
• 4. Advection Stabilization
• 5. Pressure Stabilization
  • 5.1. The Role of \(\dot m\)
• 6. RTE Stabilization
  • 6.1. Definition of the test function
  • 6.2. The form of \(\tau\)
  • 6.3. Pure Edge-based Upwind Method
  • 6.4. Finite Element SUPG Form
• 7. Nonlinear Stabilization Operator (NSO)
  • 7.1. NSO Based on Kinetic Energy Residual
  • 7.2. Local or Projected NSO Diffusive Flux Coefficient
  • 7.3. General Findings
  • 7.4. NSO as a Turbulence Model
• 8. Turbulence Modeling
  • 8.1. Standard Smagorinsky LES Model
  • 8.2. Wall Adapting Local Eddy-Viscosity, WALE
  • 8.3. One Equation \(k^{sgs}\)
  • 8.4. RANS Models
  • 8.5. Hybrid RANS/LES Models
  • 8.6. Wall Models
• 9. Supported Boundary Conditions
  • 9.1. Inflow Boundary Condition
  • 9.2. Wall Boundary Conditions
  • 9.3. Atmospheric Boundary Layer Surface Conditions
  • 9.4. Atmospheric Boundary Layer Top Conditions
  • 9.5. Turbulent Kinetic Energy, \(k_{sgs}\) LES model
  • 9.6. SST of the Atmospheric Boundary Layer
  • 9.7. AMS of the Atmospheric Boundary Layer
  • 9.8. Open Boundary Condition
  • 9.9. Strong Symmetry Boundary Condition
  • 9.10. Weak Symmetry Boundary Condition
  • 9.11. Periodic Boundary Condition
  • 9.12. Non-conformal Boundary Condition
• 10. Overset
  • 10.1. Overset Grid Assembly using Native STK Search
  • 10.2. Overset Grid Assembly using TIOGA
• 11. Property Evaluations
  • 11.1. Density
  • 11.2. Viscosity
  • 11.3. Specific Heat
  • 11.4. Lame Properties
• 12. Coupling Approach
  • 12.1. Errors due to Splitting and Stabilization
• 13. Time discretization
• 14. Multi-Physics
• 15. Wind Energy Modeling
  • 15.1. Governing Equations
  • 15.2. Turbulence Modeling
  • 15.3. Numerical Discretization & Stabilization
  • 15.4. Time stepping scheme
  • 15.5. Initial & Boundary Conditions
  • 15.6. Wind Turbine Modeling
• 16. Topological Support
• 17. Adaptivity
  • 17.1. Prolongation and Restriction
• 18. Code Abstractions
  • 18.1. Sierra Toolkit Abstractions
  • 18.2. High Level Nalu-Wind Abstractions