Full space‐time adaptive method based on collocation strategy and implicit multirate time stepping

In this paper, we present a full space‐time Adaptive Fup Collocation Method (AFCM) for solving initial‐boundary value problems with particular application on advection‐dominated advection‐diffusion problems. The spatial adaptive strategy dynamically changes the computational grid at each global time...

Full description

Saved in:
Bibliographic Details
Published in:International journal for numerical methods in fluids 2021-05, Vol.93 (5), p.1606-1626
Main Authors: Malenica, Luka, Gotovac, Hrvoje
Format: Article
Language:English
Subjects:
Accuracy
Adaptive algorithms
Advection
advection‐diffusion
advection‐dominated problems
Boundary value problems
collocation approach
Collocation methods
Computational grids
Computer applications
Discretization
implicit local time stepping
multiresolution analysis
Oscillations
Time dependence
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we present a full space‐time Adaptive Fup Collocation Method (AFCM) for solving initial‐boundary value problems with particular application on advection‐dominated advection‐diffusion problems. The spatial adaptive strategy dynamically changes the computational grid at each global time step, while the adaptive time‐marching algorithm uses different local time steps for different collocation points based on temporal accuracy criteria. Contrary to the existing space‐time adaptive methods that are based on explicit temporal discretization and scale‐dependent local time stepping, the presented method is implicit and resolves all spatial and temporal scales independently of each other. This means that smaller local time steps are used only for spatial zones where temporal solution changes are intensive, which are not necessarily the zones with finest spatial discretization. In this manner, the computationally efficient full space‐time adaptive strategy accurately resolves small‐scale features and controls numerical error and spurious oscillations. The efficiency and accuracy of AFCM are verified with some classical one‐ and two‐dimensional benchmark test cases. An Adaptive Fup Collocation Method (AFCM) that is adaptive both in space and time was developed. The method is implicit and resolves all spatial and temporal scales independently to each other. The CPU speedup was up to 5 when compared with classical space adaptive algorithm and up to 37 when compared with nonadaptive finite difference solution.
ISSN:0271-2091
1097-0363
DOI:10.1002/fld.4944