Unlike previous approaches which bootstrap the moving grid from a lower-order, finite-difference discretization, this work uses a consistent spectral collocation discretization for both the grid movement problem and the underlying, physical partial differential equation.
A self-adaptive moving grid method is implemented for MOL discretization by means of finite-difference and finite-volume schemes.
The dynamic PBE is numerically solved in both the continuous and its equivalent discrete form using the Galerkin on finite elements method (GFEM) and the moving grid technique (MGT) of Kumar and Ramkrishna [1997. Chemical Engineering Science 52, 4659 4679], respectively.
The methods employs a moving grid technique and a projection scheme based on low-order Crouzeix Raviart and P1 finite elements.
The extension of the immersed-boundary forces from the moving grid to the fixed fluid grid and the restriction of the fluid velocities from the fixed fluid grid to the moving grid have been modified to be second-order accurate.
A uniform grid is then deformed to a moving grid with desired cell volume distribution at each time.
An r-adaptive method or moving grid technique relocates a grid so that it becomes concentrated in the desired region.
Precisely, we report the results of numerical calculations of optimal moving grids for piecewise linear finite element approximation of PDE solutions in the least-squares norm.
The flow field is computed by solving a finite volume approximation of the Navier Stokes equations on moving grids augmented by turbulence models.
