Statistical conservation laws for scalar model problems: Hierarchical evolution equations
Qian Huang, Christian Rohde
TL;DR
This paper introduces hierarchical evolution equations for probability density functions in scalar conservation laws with random initial data, providing new frameworks to analyze statistical correlations and aid in closure strategies.
Contribution
It develops novel hierarchical equations for PDFs of scalar conservation laws, extending previous work on Navier-Stokes to simpler model problems.
Findings
Hierarchies capture statistical correlations effectively.
Frameworks facilitate closure strategies for PDFs.
Applicable to scalar conservation laws with random initial conditions.
Abstract
The probability density functions (PDFs) for the solution of the incompressible Navier-Stokes equation can be represented by a hierarchy of linear equations. This article develops new hierarchical evolution equations for PDFs of a scalar conservation law with random initial data as a model problem. Two frameworks are developed, including multi-point PDFs and single-point higher-order derivative PDFs. These hierarchies capture statistical correlations and guide closure strategies.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsModel Reduction and Neural Networks · Probabilistic and Robust Engineering Design · Meteorological Phenomena and Simulations