핵심 개념
Implicit solvers for atmospheric models are accelerated via Helmholtz preconditioning, ensuring stability and efficiency in solving compressible Euler equations.
초록
The content discusses the application of Helmholtz preconditioning for compressible Euler equations in atmospheric models. It introduces a novel preconditioner for the compressible Euler equations with a flux form representation of potential temperature on the Lorenz grid using mixed finite elements. The formulation allows for spatial discretizations conserving energy and potential temperature variance. The article compares different formulations of the Helmholtz operator for a dry compressible atmosphere, focusing on vertical placements of potential temperature and different forms of the potential temperature transport equation within mixed finite element spatial discretizations. It also explores the benefits and drawbacks of various modeling choices, such as collocating thermodynamic variables with pressure or vertical velocity. The study includes numerical experiments in 1D and 2D configurations to verify the stability and efficiency of the new preconditioner.
1. Introduction
Implicit solvers are crucial for stable atmospheric models.
Preconditioning accelerates the solution of compressible Euler equations.
2. Mixed Finite Element Discretization
Mixed finite element method used for spatial discretization.
Discrete variational form derived for the system.
3. Helmholtz Preconditioning
Block preconditioner introduced for the compressible Euler equations.
Comparison with existing preconditioners for different grid configurations.
4. Results
Numerical experiments conducted to verify the new preconditioner.
Stability and efficiency assessed in 1D and 2D atmospheric simulations.
통계
알고리즘은 Julia 프로그래밍 언어로 구현됨.
2D 실험에서 GridapDistributed 패키지 사용하여 병렬화 구현.
Gadi petascale 슈퍼컴퓨터에서 수치 실험 실행.
인용구
"Preconditioning accelerates the solution of compressible Euler equations."
"Numerical experiments conducted to verify the new preconditioner."