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Coupled Continuous-Discontinuous Galerkin Finite Element Solver for Compound Flood Simulations

Chayanon Wichitrnithed, Eirik Valseth, Shintaro Bunya, Ethan J. Kubatko, Clint Dawson

Abstract

Several recent tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead to effects that cannot be correctly modeled by simple superposition of its distinctive sources. In an effort to develop accurate numerical simulations of runoff, surge, and compounding floods, we develop a locally conservative coupled DG-CG discretization of the shallow water equations and integrate it into the Advanced Circulation Model (ADCIRC). We also modify the continuity equation to include spatially and temporally variable rainfall into the model using parametric rainfall models. We demonstrate the capabilities of the scheme though a sequence of physically relevant numerical tests, including small scale test cases based on laboratory measurements and large scale experiments with Hurricane Harvey in the Gulf of Mexico. The results highlight the conservation properties and robustness of the developed method and show the potential of compound flood modeling using our approach.

Coupled Continuous-Discontinuous Galerkin Finite Element Solver for Compound Flood Simulations

Abstract

Several recent tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead to effects that cannot be correctly modeled by simple superposition of its distinctive sources. In an effort to develop accurate numerical simulations of runoff, surge, and compounding floods, we develop a locally conservative coupled DG-CG discretization of the shallow water equations and integrate it into the Advanced Circulation Model (ADCIRC). We also modify the continuity equation to include spatially and temporally variable rainfall into the model using parametric rainfall models. We demonstrate the capabilities of the scheme though a sequence of physically relevant numerical tests, including small scale test cases based on laboratory measurements and large scale experiments with Hurricane Harvey in the Gulf of Mexico. The results highlight the conservation properties and robustness of the developed method and show the potential of compound flood modeling using our approach.

Paper Structure

This paper contains 27 sections, 50 equations, 18 figures, 6 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Governing Equations
  3. The Generalized Wave Continuity Equation
  4. Discontinuous and Continuous Galerkin Discretization
  5. Continuity Equation
  6. Numerical Flux and Boundary Conditions
  7. Momentum Equation
  8. Coupling between different solution spaces
  9. Summary of DG and CG discretization
  10. Wetting and Drying
  11. CG approach
  12. DG approach
  13. Combined approach
  14. Incorporating Rainfall Data
  15. Numerical Experiments
  16. ...and 12 more sections

Figures (18)

  • Figure 1: Definition of shallow water elevations. The horizontal line denotes the geoid, where $\zeta = h_b = 0$.
  • Figure 2: Definition of a triangular element $\Omega_e$
  • Figure 3: Usage of the R-CLIPER parametric model.
  • Figure 4: Domain and boundary conditions of the Lynch and Gray test case.
  • Figure 5: $h-$convergence in surface elevation (left) and $u_x$ (right) for the Lynch and Gray test case.
  • ...and 13 more figures