The paper investigates the problem of adaptive planning and control of a generalized computational experiment in mathematical modeling of real physical processes. A generalized computational experiment implies a multiple solution of the numerical simulation problem for different sets of values of defining model parameters. A general structure of a control model for a generalized computational experiment is proposed, the concept of the state of experiment is introduced, and a mechanism for evaluating its effectiveness is considered. A description of the concepts of reliability, representativeness, and efficiency for a generalized computational experiment is introduced. A detailed description of the algorithm for calculating the effectiveness of a generalized computational experiment based on the analysis of series of approximating curves built on subsets of modeling parameters is given. An example is given of determining the effectiveness of the state of a generalized computational experiment when assessing the accuracy of numerical models of the OpenFOAM software platform for a three-dimensional problem of inviscid flow around a cone.