Theory and Formulation

This section presents the theoretical foundation and mathematical formulation of the ADCIRC (ADvanced CIRCulation) model. The content is based on the ADCIRC theory document (2004) and other publications.

Contents:

• Governing Equations
  • Continuity Equation
  • Momentum Equations
  • Bottom Stress Formulation
• Numerical Implementation
  • Finite Element Spatial Discretization
  • Weak Formulation and Assembly
  • Time Discretization
  • Lumped Mass Matrix
  • Stabilization Techniques
• Boundary Conditions
  • External Boundary Conditions
  • Internal Boundary Conditions
  • Surface Boundary Conditions
• Wave Continuity Formulation
  • Derivation of the GWCE
  • Advantages of the GWCE
  • Role of the Tau Parameter
• Coordinate Systems
  • Spherical Coordinates
  • Cartesian Coordinates
  • Coordinate Transformations
  • CPP Coordinate System
  • Vertical Coordinate Systems
• Wetting and Drying
  • Conceptual Approach
  • Basic Algorithm
  • Numerical Techniques
  • Implementation Details
• Baroclinic Terms
  • Density Variation
  • Baroclinic Pressure Gradient
  • Transport Equations
  • Three-Dimensional Formulation
  • Surface Heat Flux
  • Numerical Considerations for Baroclinic Simulations