We developed computational method using higher-order basis functions in order to use phase field model. We can not apply Non-Uniform Rational B-spline (NURBS) which is used in computational analysis in recent years to phase field model.

Therefore, we use T-spline which is superset of NURBS for this problem.

Though T-spline is known as mathematical model, there are few examples applied for computational analysis. Then we provided Truncated Hierarchical NURBS (THN) which is one of T-spline, and suitable for computational analysis.

We implemented THN is capable of local refinement and non-uniform refinement.

This technique is necessary for fluid computations to resolve the flows around object.

As we progress the research about THN, we found that it is important how to define the element length for space--time method with isogeometric discretizations.

Then, we have studied about appropriate element length for smooth basis functions. We provided new stabilization parameters, and showed that gives us good solutions. We submitted the paper for these results, and it has already accepted ([1]).