Supplementary variable method for thermodynamically consistent partial differential equations

We present a paradigm for developing thermodynamical consistent numerical algorithms thermodynamically partial differential equation (TCPDE) systems, called the supplementary variable method (SVM). add proper number of variables to TCPDE system coupled with its energy and other deduced equations through perturbations arrive at consistent, well-determined, solvable structurally stable system. The extended not only reduces specific values variables, but also allows one retain consistency solvability after approximation. Among virtually infinite many possibilities we two that maintain in before A pseudo-spectral is used space fully discrete schemes. new schemes are compared SAV scheme implicit Crank–Nicolson scheme. results favor overall performance.