A new TVD method for advection simulation on 2D unstructured grids

Abstract

SUMMARYFor advection schemes with flux limiters derived on one‐dimensional grids to two‐dimensional (2D) unstructured triangular ones. In this method, the variables located normal to this face are taken into more account to compute the flux, by means of defining required nodes along the line through the center point of the considered face and perpendicular to it. Besides, the new method adopts the improved total variation diminishing schemes in, which consider the face position between the two neighboring cells as well as the size differences of the related cells; therefore, it fits 2D unstructured grids well. Compared with the present flux limiting methods for 2D unstructured grids, a higher accuracy and efficiency and a good monotonicity are achieved by the new method.Copyright © 2012 John Wiley & Sons, Ltd.

A 2D extension of a Large Time Step explicit scheme (CFL>1) for unsteady problems with wet/dry boundaries

“…Firstly, the peak value, one indicator of the accuracy of the numerical solution, increases because the time step size is bigger and fewer steps are required to compute the solution. It is worth remarking that the numerical results improve on those obtained in [16] where a sophisticated 2D TVD method is used. On the other hand, the solution is deviating due to the non-uniform velocity field.…”

“…A square 2 m × 2 m domain discretized using 8 464 cells (92 × 92) is used as a quadrilateral structured mesh to simulate the circular advection of a "cone" defined as follows [16]: …”

TVD differencing on three-dimensional unstructured meshes with monotonicity-preserving correction of mesh skewness

“…(1) develops severe oscillations on the upwind-side of the discontinuities, whereas the iterative algorithm preserves the monotonicity of the solution. Such oscillations have been reported, without a comprehensive explanation, in a number of studies using the SUPERBEE scheme [8][9][10][11]. Examining the flux limiter of the SUPERBEE scheme in the Sweby diagram, see For the results presented in Fig.…”

“…This is a simplification of the multidimensional applications typically found in heat and mass transfer as well as fluid dynamics. Furthermore, the non-linearity inherently introduced by TVD differencing [7], since the choice of differencing scheme is dependent on the advected scalar field, is a frequently overlooked issue in the relevant literature, even though oscillations caused by compressive TVD schemes reported in previous studies [8][9][10][11] may be attributed to this non-linearity.…”

Numerical error control for second-order explicit TVD scheme with limiters in advection simulation

“…where n c is the cell number [11,34]. The second-order TVD schemes with the MIN_MOD, Van Leer and SUPERBEE limiters as well as the FOU scheme are tested in 1D cases with value's distributions shaped in isosceles triangles, symmetric parabolic and cosine curves ( Fig.…”