An Adaptive TVD Limiter

An adaptive TVD limiter, based on a limiter approximating the upper boundary of the TVD range and that of the third-order upwind TVD scheme, is developed in this work. The limiter switches to the comprressive limiter near a discontinuity, to the third-order TVD scheme's limiter in the smooth region, and to a weighted averaged scheme in the transition region between smooth and high gradient solutions. Numerical experiments show that the proposed scheme works very well for one-dimensional scalar equation problems but becomes less effective in one- and two-dimensional Euler equation problems. Further study is required for the two-dimensional scalar equation problems.