2020
DOI: 10.1002/fld.4935
|View full text |Cite
|
Sign up to set email alerts
|

Accuracy aspects of conventional discretization methods for scalar transport with nonzero divergence velocity field arising from the energy balance equation

Abstract: We are concerned with the numerical solution of a linear transport problem with nonzero divergence velocity field that originates from the spectral energy balance equation describing the evolution of wind waves and swells in coastal seas. The discretization error of the commonly used first‐order upwind finite difference and first‐order vertex‐centered upwind finite volume schemes in one space dimension is analyzed. Smoothness of nondivergent velocity field plays a crucial role in this. No such analysis has bee… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
3
2

Citation Types

0
9
0

Year Published

2021
2021
2022
2022

Publication Types

Select...
2

Relationship

1
1

Authors

Journals

citations
Cited by 2 publications
(9 citation statements)
references
References 18 publications
0
9
0
Order By: Relevance
“…Without the ambient current, it equals the wave group velocity. The importance of the effect of irregularity of this nondivergent field is highlighted in [36].…”
Section: Discrete Calculus Discretizationsmentioning
confidence: 99%
See 4 more Smart Citations
“…Without the ambient current, it equals the wave group velocity. The importance of the effect of irregularity of this nondivergent field is highlighted in [36].…”
Section: Discrete Calculus Discretizationsmentioning
confidence: 99%
“…The resulting discrete equation is consistent with transport Equation (5). This scheme for unstructured meshes is the same as the first order vertex-centered upwind finite volume scheme described in [36]. Finally, the first order implicit Euler method is adopted for time discretization, since the action balance equation is known to be rather stiff [39].…”
Section: Discretization Based On Discrete 2-formmentioning
confidence: 99%
See 3 more Smart Citations