High performance numerical simulation programs are widely used to simulate actual physical processes on high performance computers for the analysis of various physical and engineering problems. They are usually regarded as non-testable due to their high complexity. This paper reports our real experience and lessons learned from testing five simulation programs that will be used to design and analyze nuclear power plants. We applied five testing approaches and found 33 bugs. We found that property-based testing and metamorphic testing are two effective methods. Nevertheless, we suffered from the lack of domain knowledge, the high test costs, the shortage of test cases, severe oracle issues, and inadequate automation support. Consequently, the five programs are not exhaustively tested from the perspective of software testing, and many existing software testing techniques and tools are not fully applicable due to scalability and portability issues. We need more collaboration and communication with other communities to promote the research and application of software testing techniques.