Matrix Analysis of Tracer Transport

TL;DR

This paper reviews matrix methods for modeling tracer transport, highlighting their suitability for linear systems, and discusses their applications in Eulerian simulations, deformation analysis, and stability improvements.

Contribution

It provides a comprehensive review of matrix approaches to tracer transport, including derivations and properties, enhancing understanding of their use in linear Eulerian systems.

Findings

Matrix methods effectively model linear tracer transport.

Matrix approaches aid in analyzing deformation in Lagrangian space.

They help improve numerical stability in simulations.

Abstract

We review matrix methods as applied to tracer transport. Because tracer transport is linear, matrix methods are an ideal fit for the problem. A gridded, Eulerian tracer simulation can be approximated as a system of linear ordinary differential equations (ODEs). The first-order stretching and deformation of Lagrangian space can also be calculated using a system of linear ODEs. Solutions to these equations are reviewed as well as special properties. Using matrices to model Eulerian tracer transport can also help understand and improve the stability of numerical solutions. Detailed derivations are included.