TY - JOUR

T1 - Mimetic finite differences for boundaries misaligned with grid nodes

AU - Belousov, Danila

AU - Lisitsa, Vadim

N1 - Danila Belousov derived the formulae and performed the numerical experiments. Vadim Lisitsa did the problem statement and verified the results under the support of the RSCF grant no. 22-11-00004 .

PY - 2023/8/15

Y1 - 2023/8/15

N2 - This paper considers the problem of mimetic staggered-grid finite difference scheme construction in the case of a boundary misaligned with the grid points. We show that depending on the reciprocal positions of the nearest grid point and whether the point is inside or outside the domain, two cases should be considered separately. In both cases, we present general rules to construct the mimetic difference operators to approximate the gradient and divergence operators. In addition, we investigate the stability criterion of the explicit in time scheme, which employs derived operators to approximate spatial derivatives. We show that, depending on the reciprocal positions of the nearest grid point, the Courant number may be smaller by 7% than that of the initial value problem approximation.

AB - This paper considers the problem of mimetic staggered-grid finite difference scheme construction in the case of a boundary misaligned with the grid points. We show that depending on the reciprocal positions of the nearest grid point and whether the point is inside or outside the domain, two cases should be considered separately. In both cases, we present general rules to construct the mimetic difference operators to approximate the gradient and divergence operators. In addition, we investigate the stability criterion of the explicit in time scheme, which employs derived operators to approximate spatial derivatives. We show that, depending on the reciprocal positions of the nearest grid point, the Courant number may be smaller by 7% than that of the initial value problem approximation.

KW - Mimetic finite differences

KW - Stability condition

KW - Staggered grid scheme

UR - https://www.scopus.com/record/display.uri?eid=2-s2.0-85149979311&origin=inward&txGid=61bfdfd40b7c864494831a2f24152749

UR - https://www.mendeley.com/catalogue/971b240e-fb5c-314f-8c53-6e28ff6b54f5/

U2 - 10.1016/j.cam.2023.115185

DO - 10.1016/j.cam.2023.115185

M3 - Article

VL - 428

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

SN - 0377-0427

M1 - 115185

ER -