A revisit of the energy quadratization method with a relaxation technique

This letter revisits the energy quadratization (EQ) method by introducing a novel and essential relaxation technique to improve its accuracy consistency. The EQ has witnessed significant popularity in past few years. Though we acknowledge effectiveness designing energy-stable schemes for thermodynamically consistent models, primary known drawback is apparent, i.e., it respects “modified” law represented auxiliary variables instead of original variables. Truncation errors are introduced during numerical calculations so that solutions no longer equivalent their continuous definitions. Even though dissipation respected solutions, not guaranteed. In this letter, overcome inconsistency step, which named relaxed-EQ (REQ) method. computational cost step negligible compared with baseline Meanwhile, REQ holds all method’s good properties, such as linearity unconditionally stability. Then apply several widely-used phase field models highlight effectiveness.