To solve the L2-gradient flow-based phase-field crystal equation accurately and efficiently, we present a linear, second-order, and unconditionally energy-stable method. We first truncate the quartic function in the Swift–Hohenberg energy functional. We also put the truncated function in the expansive part of the energy and add an extra term to have a linear convex splitting. Then, we apply the linear convex splitting to both the L2-gradient flow and the nonlocal Lagrange multiplier terms and

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... mbine it with the second-order SSP-IMEX-RK method. We prove that the proposed method is mass-conservative and unconditionally energy-stable. Numerical experiments including standard tests in the classical H−1-gradient flow-based phase-field crystal equation support that the proposed method is second-order accurate in time, mass conservative, and unconditionally energy-stable.