Compiler automatic optimization and parallelization techniques are well suited for some classes of simulation or signal processing applications, however they usually don't take into account domain-specific knowledge nor the possibility to change or to remove some computations to achieve " good enough " results. Quite differently, production simulation and signal processing codes have adaptive capabilities: they are designed to compute precise results only where it matters if the complete problem is not tractable or if computation time must be short. In this paper, we present a new way to provide adaptive capabilities to compute-intensive codes automatically. It relies on domain-specific knowledge provided through special pragmas by the programmer in the input code and on polyhedral compilation techniques to continuously regenerate at runtime a code that performs heavy computations only where it matters at every moment. We present a case study on a fluid simulation application where our strategy enables significant computation savings and speedup in the optimized portion of the application while maintaining a good precision, with a minimal effort from the programmer.