The CIP/CCUP (constraint interpolation profile/CIP combined, unified procedure) method is combined in this research with the adaptive half-staggered-type Soroban grid. The recently developed Soroban grid allows the CIP/CCUP method to achieve even more powerful computation. The meshless particles in the Soroban grid move freely along the axes and the axes move freely on a plane. Similarly, the planes move along the imaginary axes following the adaptivity rule. However, there are inherent complexity and the computational burden arising from the staggered grid type when the meshless concept is involved. Therefore, the Soroban grid method has been developed in a collocated grid form. In this research, a simple half-staggered grid concept is introduced to minimize the complexity. The half-staggered grid employs velocity meshes in addition to the pressure or density grid in each direction and the movement of velocity meshes is restricted by the pressure or density grid. The new grid has been tested and validated by repeating the benchmark forward-facing step problem in a Mach 3 channel and strong 2-D explosion test. A strong and stable coupling between pressure and velocity comparable to that in the typical staggered approach was attained in the meshless half-staggered grid in spite of the meshless feature of the Soroban grid. (C) 2010 Elsevier Ltd. All rights reserved.