A third-order temporal accurate and unconditionally stable Runge-Kutta scalar auxiliary variable method for the modified phase field crystal model

We present a third-order time-accurate Runge-Kutta scalar auxiliary variable algorithm for simulating the modified phase field crystal equation with long-range interaction. This method guarantees mass conservation and unconditional energy stability. By combining with the Fourier spectral method, we design a new numerical method to enhance computational efficiency. This scheme is proven to possess third-order temporal accuracy. We prove that the proposed computational method satisfies discrete mass conservation and energy dissipation. Several numerical tests are conducted to verify the performance of the proposed numerical algorithm.