Text

Conservation Laws for Free-Boundary Fluid Layers

Time-dependent models of fluid motion in thin layers, subject to signed source terms, represent important subproblems within climate dynamics. Examples include ice sheets, sea ice, and even shallow oceans and lakes. We address these problems as discrete-time sequences of continuous-space weak formulations, namely, (monotone) variational inequalities or complementarity problems, in which the conserved quantity is the layer thickness. Free boundaries wherein the thickness and mass flux both go to zero at the margin of the fluid layer generically arise in such models. After showing these problems are well-posed in several cases, we consider the limitations to discrete conservation in numerical schemes. A free boundary in a region of negative source---an ablation-caused margin---turns out to be a barrier to exact conservation in either a continuous- or discrete-space sense. We then propose computable a posteriori quantities which allow conservation-error bounds in finite volume and finite element schemes.

Ketersediaan

Informasi Detail

Judul Seri

SIAM JOURNAL ON APPLIED MATHEMATICS; Vol.81 No.5 September - October 2021

No. Panggil

-

Penerbit

: .,

Deskripsi Fisik

p. 2007 - 2032

Bahasa

English

ISBN/ISSN

-

Klasifikasi

NONE

Tipe Isi

-

Tipe Media

-

Tipe Pembawa

-

Edisi

-

Subjek

NUMERICAL ANALYSIS
FLUID DYNAMICS
VARIATIONAL INEQUALITY
CONSERVATION LAW
CLIMATE MODELING

Info Detail Spesifik

https://doi.org/10.1137/20M135217X

Pernyataan Tanggungjawab

Ed Bueler

Versi lain/terkait

Lampiran Berkas

Komentar