We propose a post-processing method for Q-tensor dynamics, which constrains the eigenvalues of Q within the physical range \((-1/3,2/3)\) by incorporating a projection into the time stepping. We show that the projection keeps the eigenframe invariant, from which we derive the explicit formula for the projection that enables easy implementations. Provided that the exact solution lies within the physical range, the projection ensures that the error does not increase. As a result, when the projection is built in a class of stable single-step linearly semi-implicit schemes as post-processing, we establish the error estimates, illustrated by a gradient flow keeping the physical range of Q. In numerical examples, we examine some defect dynamics for nematic liquid crystals, and the performance of post-processing schemes together with an adaptive time-stepping strategy specially designed with the projection.
