TY - JOUR
T1 - Resolving small-scale structures in Boussinesq convection by adaptive grid methods
AU - Zhang, Zhengru
AU - TANG, Tao
N1 - Funding Information:
The research of the authors was supported by the Hong Kong Research Grants Council (Hong Kong RGC Grant 2033/99P).
PY - 2006/10/15
Y1 - 2006/10/15
N2 - Inviscid Boussinesq convection is a challenging problem both analytically and numerically. Due to the complex dynamic development of small scales and the rapid loss of solution regularity, the Boussinesq convection pushes any numerical strategy to the limit. In E and Shu (Phys. Fluids 6 (1994) 49), a detailed numerical study of the Boussinesq convection in the absence of viscous effects is carried out using filtered pseudospectral method and a high-order accurate ENO schemes. In their computations, very fine grids have to be used in order to resolve the small-structures of the Boussinesq fluid. In this work, we will develop an efficient adaptive grid method for solving the inviscid incompressible flows, which can be useful in resolving extremely small-structures with reasonably small number of grid points. To demonstrate the effectiveness of the proposed method, the Boussinesq convection problem will be computed using the adaptive grid method.
AB - Inviscid Boussinesq convection is a challenging problem both analytically and numerically. Due to the complex dynamic development of small scales and the rapid loss of solution regularity, the Boussinesq convection pushes any numerical strategy to the limit. In E and Shu (Phys. Fluids 6 (1994) 49), a detailed numerical study of the Boussinesq convection in the absence of viscous effects is carried out using filtered pseudospectral method and a high-order accurate ENO schemes. In their computations, very fine grids have to be used in order to resolve the small-structures of the Boussinesq fluid. In this work, we will develop an efficient adaptive grid method for solving the inviscid incompressible flows, which can be useful in resolving extremely small-structures with reasonably small number of grid points. To demonstrate the effectiveness of the proposed method, the Boussinesq convection problem will be computed using the adaptive grid method.
KW - Adaptive mesh method
KW - Boussinesq convection
KW - Finite volume method
KW - Incompressible flow
UR - http://www.scopus.com/inward/record.url?scp=33747003233&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2005.03.087
DO - 10.1016/j.cam.2005.03.087
M3 - Journal article
AN - SCOPUS:33747003233
SN - 0377-0427
VL - 195
SP - 274
EP - 291
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
IS - 1-2
ER -