A Parameter-Free Dynamic Alternative to Hyper-Viscosity for Coupled Transport Equations: Application to the Simulation of 3D Squall Lines Using Spectral Elements

Abstract

The stabilization of high order spectral elements to solve the transport equations for tracers in the atmosphere remains an active topic of research among atmospheric modelers. This paper builds on our previous work on variational multiscale stabilization (VMS) and discontinuity capturing (DC) [Variational multiscale stabilization of high-order spectral elements for the advection-diffusion equation J. Comput. Phys. 231 (2012) 7187-7213] and shows the applicability of VMS+DC to realistic atmospheric problems that involve physics coupling with phase change in the simulation of 3D deep convection. We show that the VMS+DC approach is a robust technique that can damp the high order modes characterizing the spectral element solution of complex coupled transport problems. The method has important properties that techniques of more common use often lack 1) it is free of a user-defined parameter, 2) it is anisotropic in that it only acts along the ow direction, 3) it is numerically consistent, and 4) it can improve the monotonicity of high-order spectral elements. The proposed method is assessed by comparing the results against those obtained with a fourth-order hyper-viscosity programmed in the same code. The main conclusion that arises is that tuning can be fully avoided without loss of accuracy if the dissipative scheme is properly designed. Finally, the cost of parallel communication is that of a second order operator which means that fewer communications are required by VMS+DC than by a hyper-viscosity method fewer communications translate into a faster and more scalable code, which is of vital importance as we approach the exascale range of computing.

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Document Details

Document Type
Technical Report
Publication Date
Jun 04, 2015
Accession Number
ADA627039

Entities

People

  • Francis Giraldo
  • Simone Marras

Organizations

  • Naval Postgraduate School

Tags

DTIC Thesaurus Topics

  • Accuracy
  • Advection
  • Atmospheres
  • Boltzmann Equation
  • Boundary Layer
  • Buoyancy
  • Computational Fluid Dynamics
  • Computational Science
  • Convection
  • Diffusion
  • Discontinuities
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Fluid Flow
  • Simulations
  • Three Dimensional

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Ocean-Atmosphere Mesoscale Modeling, Data Assimilation, and Flux Boundary Layers