We present a new approach for simulation of unsteady flow problems that include interaction between different time-scale phenomena. Such problems require computations that capture the details in the short time scale and span over long time periods to represent the long time-scale phenomena. However, it is hard to obtain such solutions in a reasonable amount of computing time. In such cases, typically longer time-scale phenomena are ignored or assumed not to change while the short time-scale phenomena are computed.

We propose to use space--time (ST) computational methods with isogeometric discretization, giving us higher-order accuracy in space and time. In the ST methods and other stabilized methods, an embedded stabilization parameter plays an important role. This parameter involves a measure of the local length scale. The length definitions have been discussed earlier in finite element discretizations. These definitions are often used also in isogeometric discretization.

In this research, we implement space--time computation techniques with continuous representation in time. The test computations we present show the value of the new method in obtaining better computation efficiency and solution accuracy.