A versatile, orthogonal adaptive grid scheme for two-dimensional numerical fluid dynamics and heat transfer problems is presented. The scheme employs a one-dimensional adaptation sweep to define one family of physical grid lines. A second sweep then uses a technique called AOT, developed herein, to fit an orthogonal family of lines to the solution-adapted lines. These procedures are fast, require.little core storage, and do not change the original domain boundaries. Each subroutine developed performs a specific function and together they form the adaptive grid module. The versatility of these subroutines allows their usage in various combinations and in either grid direction. Modifications required to implement this scheme into existing fluid dynamics and heat transfer codes, therefore, are minimal. Code documentation and sample applications showing the implementation and versatility of the scheme are presented.