Matches in SemOpenAlex for { <https://semopenalex.org/work/W2072179411> ?p ?o ?g. }
Showing items 1 to 91 of
91
with 100 items per page.
- W2072179411 endingPage "669" @default.
- W2072179411 startingPage "654" @default.
- W2072179411 abstract "Recent advances in the collection of Lagrangian data from the ocean and results about the well-posedness of the primitive equations have led to a renewed interest in solving flow equations in Lagrangian coordinates. We do not take the view that solving in Lagrangian coordinates equates to solving on a moving grid that can become twisted or distorted. Rather, the grid in Lagrangian coordinates represents the initial position of particles, and it does not change with time. We apply numerical methods traditionally used to solve differential equations in Eulerian coordinates, to solve the shallow water equations in Lagrangian coordinates. The difficulty with solving in Lagrangian coordinates is that the transformation from Eulerian coordinates results in solving a highly nonlinear partial differential equation. The non-linearity is mainly due to the Jacobian of the coordinate transformation, which is a precise record of how the particles are rotated and stretched. The inverse Jacobian must be calculated, thus Lagrangian coordinates cannot be used in instances where the Jacobian vanishes. For linear (spatial) flows we give an explicit formula for the Jacobian and describe the two situations where the Lagrangian shallow water equations cannot be used because either the Jacobian vanishes or the shallow water assumption is violated. We also prove that linear (in space) steady state solutions of the Lagrangian shallow water equations have Jacobian equal to one. In the situations where the shallow water equations can be solved in Lagrangian coordinates, accurate numerical solutions are found with finite differences, the Chebyshev pseudospectral method, and the fourth order Runge–Kutta method. The numerical results shown here emphasize the need for high order temporal approximations for long time integrations." @default.
- W2072179411 created "2016-06-24" @default.
- W2072179411 creator A5069055446 @default.
- W2072179411 date "2004-11-01" @default.
- W2072179411 modified "2023-09-26" @default.
- W2072179411 title "The shallow water equations in Lagrangian coordinates" @default.
- W2072179411 cites W1975981118 @default.
- W2072179411 cites W1997391491 @default.
- W2072179411 cites W2008967942 @default.
- W2072179411 cites W2012631405 @default.
- W2072179411 cites W2012680455 @default.
- W2072179411 cites W2031443432 @default.
- W2072179411 cites W2033318187 @default.
- W2072179411 cites W2061392384 @default.
- W2072179411 cites W2073257715 @default.
- W2072179411 cites W2103768683 @default.
- W2072179411 cites W2153751391 @default.
- W2072179411 doi "https://doi.org/10.1016/j.jcp.2004.04.014" @default.
- W2072179411 hasPublicationYear "2004" @default.
- W2072179411 type Work @default.
- W2072179411 sameAs 2072179411 @default.
- W2072179411 citedByCount "7" @default.
- W2072179411 countsByYear W20721794112012 @default.
- W2072179411 countsByYear W20721794112015 @default.
- W2072179411 countsByYear W20721794112017 @default.
- W2072179411 countsByYear W20721794112022 @default.
- W2072179411 crossrefType "journal-article" @default.
- W2072179411 hasAuthorship W2072179411A5069055446 @default.
- W2072179411 hasBestOaLocation W20721794112 @default.
- W2072179411 hasConcept C105815890 @default.
- W2072179411 hasConcept C121332964 @default.
- W2072179411 hasConcept C134306372 @default.
- W2072179411 hasConcept C140295346 @default.
- W2072179411 hasConcept C147247565 @default.
- W2072179411 hasConcept C158622935 @default.
- W2072179411 hasConcept C181830111 @default.
- W2072179411 hasConcept C200331156 @default.
- W2072179411 hasConcept C206647686 @default.
- W2072179411 hasConcept C2524010 @default.
- W2072179411 hasConcept C28826006 @default.
- W2072179411 hasConcept C31971599 @default.
- W2072179411 hasConcept C33923547 @default.
- W2072179411 hasConcept C37914503 @default.
- W2072179411 hasConcept C43058520 @default.
- W2072179411 hasConcept C53469067 @default.
- W2072179411 hasConcept C62520636 @default.
- W2072179411 hasConcept C80551277 @default.
- W2072179411 hasConcept C89901390 @default.
- W2072179411 hasConcept C97491812 @default.
- W2072179411 hasConceptScore W2072179411C105815890 @default.
- W2072179411 hasConceptScore W2072179411C121332964 @default.
- W2072179411 hasConceptScore W2072179411C134306372 @default.
- W2072179411 hasConceptScore W2072179411C140295346 @default.
- W2072179411 hasConceptScore W2072179411C147247565 @default.
- W2072179411 hasConceptScore W2072179411C158622935 @default.
- W2072179411 hasConceptScore W2072179411C181830111 @default.
- W2072179411 hasConceptScore W2072179411C200331156 @default.
- W2072179411 hasConceptScore W2072179411C206647686 @default.
- W2072179411 hasConceptScore W2072179411C2524010 @default.
- W2072179411 hasConceptScore W2072179411C28826006 @default.
- W2072179411 hasConceptScore W2072179411C31971599 @default.
- W2072179411 hasConceptScore W2072179411C33923547 @default.
- W2072179411 hasConceptScore W2072179411C37914503 @default.
- W2072179411 hasConceptScore W2072179411C43058520 @default.
- W2072179411 hasConceptScore W2072179411C53469067 @default.
- W2072179411 hasConceptScore W2072179411C62520636 @default.
- W2072179411 hasConceptScore W2072179411C80551277 @default.
- W2072179411 hasConceptScore W2072179411C89901390 @default.
- W2072179411 hasConceptScore W2072179411C97491812 @default.
- W2072179411 hasIssue "2" @default.
- W2072179411 hasLocation W20721794111 @default.
- W2072179411 hasLocation W20721794112 @default.
- W2072179411 hasOpenAccess W2072179411 @default.
- W2072179411 hasPrimaryLocation W20721794111 @default.
- W2072179411 hasRelatedWork W1984382240 @default.
- W2072179411 hasRelatedWork W2036047571 @default.
- W2072179411 hasRelatedWork W2375052559 @default.
- W2072179411 hasRelatedWork W2532747996 @default.
- W2072179411 hasRelatedWork W2556484976 @default.
- W2072179411 hasRelatedWork W2799287214 @default.
- W2072179411 hasRelatedWork W2950652093 @default.
- W2072179411 hasRelatedWork W3099360194 @default.
- W2072179411 hasRelatedWork W571515973 @default.
- W2072179411 hasRelatedWork W2217690358 @default.
- W2072179411 hasVolume "200" @default.
- W2072179411 isParatext "false" @default.
- W2072179411 isRetracted "false" @default.
- W2072179411 magId "2072179411" @default.
- W2072179411 workType "article" @default.