This thesis examines the Euler equations of gas dynamics and develops a new adaption indicator, which is based on the weak local residual measured for the non- conservative pressure variable. We demonstrate that the proposed indicator is capable of automatically detecting discontinuities and distinguishing between the shock and contact waves when they are isolated from each other. We use the developed indi- cator to design a scheme adaption algorithm, according to which nonlinear limiters are used only in the vicinity of shocks. The new adaption algorithm is realized using a second-order limited scheme and a high-order nonlimited central-upwind scheme. Robustness and high resolution of the designed method is shown on a number of one- and two-dimensional numerical examples.
