Efficient implementation of essentially non-oscillatory shock-capturing schemes,II
Journal of Computational Physics
Local adaptive mesh refinement for shock hydrodynamics
Journal of Computational Physics
Matrix-dependent prolongations and restrictions in a blackbox multigrid solver
Journal of Computational and Applied Mathematics
Adaptive grid generation from harmonic maps on Reimannian manifolds
Journal of Computational Physics
An adaptive grid with directional control
Journal of Computational Physics
Moving finite elements
An r-adaptive finite element method based upon moving mesh PDEs
Journal of Computational Physics
An efficient dynamically adaptive mesh for potentially singular solutions
Journal of Computational Physics
Moving mesh methods in multiple dimensions based on harmonic maps
Journal of Computational Physics
Adaptive Mesh Methods for One- and Two-Dimensional Hyperbolic Conservation Laws
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Moving Mesh Finite Element Methods for the Incompressible Navier--Stokes Equations
SIAM Journal on Scientific Computing
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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.