The process of establishing credibility in computational model predictions via verification and validation (V&V) encompasses a wide range of activities. Those activities are focused on collecting evidence that the model is adequate for the intended application and that the errors and uncertainties are quantified. In this work, we use the predictive capability maturity model (PCMM) as an organizing framework for evidence collection activities and summarizing our credibility assessment. We discuss our approaches to sensitivity analysis, model calibration, model validation, and uncertainty quantification and how they support our assessments in the solution verification, model validation, and uncertainty quantification elements of the PCMM. For completeness, we also include some limited assessment discussion for the remaining PCMM elements. Because the computational cost of performing V&V and the ensuing predictive calculations is substantial, we include discussion of our approach to addressing computational resource considerations, primarily through the use of response surface surrogates and multiple mesh fidelities.