The original purpose of this work is to develop a finite volume solver based on the unstructured grid generated by the commercial code, for example, ICEM. After it is successfully applied to unstructured grid, we extend our code to the adaptively refined grid in order to solve more sophisticated problems. From the test results, we are quite satisfied with the extension. Finally, for preserving the advantages of the Cartesian coordinates, we develop a new Cartesian grid system. In this grid system, the orthogonal grids near body are projected on the body to form a new element. The method also can prevent from too many different shapes of the elements near the body. A two dimensional cylinder flow is calculated and the result is amazing.