TY - JOUR

T1 - Safe zone for phase-resolved simulation of interactions between waves and vertically sheared currents

AU - Li, Tianyi

AU - Shen, Lian

PY - 2020/6

Y1 - 2020/6

N2 - In this letter, we analyze the numerical stability of a velocity-based boundary integral equation for nonlinear interactions between surface waves and vertically sheared currents and propose an upper bound for the wave elevations associated with a finite number of resolved wave modes to guarantee the convergence of the numerical solution. The upper bound is expressed as a function of the L∞ norm of dimensionless wave elevations and wave steepness. In general, energy accumulation at high wavenumbers may lead to numerical instability. The upper bound decreases as we increase the number of resolved wave modes. Furthermore, when we assume the regularity of the wave field, such as the power-law decay in the spectral domain, the upper bound becomes independent of the number of resolved wave modes when it becomes large enough, and the criteria of simulation stability are relaxed.

AB - In this letter, we analyze the numerical stability of a velocity-based boundary integral equation for nonlinear interactions between surface waves and vertically sheared currents and propose an upper bound for the wave elevations associated with a finite number of resolved wave modes to guarantee the convergence of the numerical solution. The upper bound is expressed as a function of the L∞ norm of dimensionless wave elevations and wave steepness. In general, energy accumulation at high wavenumbers may lead to numerical instability. The upper bound decreases as we increase the number of resolved wave modes. Furthermore, when we assume the regularity of the wave field, such as the power-law decay in the spectral domain, the upper bound becomes independent of the number of resolved wave modes when it becomes large enough, and the criteria of simulation stability are relaxed.

KW - Boundary integral equation

KW - Current

KW - Numerical simulation

KW - Water wave

UR - http://www.scopus.com/inward/record.url?scp=85079275132&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85079275132&partnerID=8YFLogxK

U2 - 10.1016/j.aml.2020.106272

DO - 10.1016/j.aml.2020.106272

M3 - Article

AN - SCOPUS:85079275132

VL - 104

JO - Applied Mathematics Letters

JF - Applied Mathematics Letters

SN - 0893-9659

M1 - 106272

ER -