The multi-scale coupling program for high temperature gas-cooled reactors encompasses complex physical phenomena across the microscopic, mesoscopic, and macroscopic level. Owing to the significant development expenses and the complexity of forming precise analytical solutions, making traditional testing methods invalid, verifying multi-scale codes is hindered by the oracle problem. Metamorphic testing is an effective technique to alleviate the oracle problem. This study uses a two-stage verification method grounded in metamorphic relations, following the introduction of code verification in th...