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Background: Left ventricular assist devices (LVADs) are implantable pumps that act as a life support therapy for patients with severe heart failure. Despite improving the survival rate, LVAD therapy can carry major complications. Particularly, the flow distortion introduced by the LVAD in the left ventricle (LV) may induce thrombus formation. While previous works have used numerical models to study the impact of multiple variables in the intra-LV stagnation regions, a comprehensive validation analysis has never been executed. The main goal of this work is to present a model of the LV-LVAD system and to design and follow a verification, validation and uncertainty quantification (VVUQ) plan based on the ASME V&V40 and V&V20 standards to ensure credible predictions. Methods: The experiment used to validate the simulation is the SDSU cardiac simulator, a bench mock-up of the cardiovascular system that allows mimicking multiple operation conditions for the heart-LVAD system. The numerical model is based on Alya, the BSC's in-house platform for numerical modelling. Alya solves the Navier-Stokes equation with an Arbitrary Lagrangian-Eulerian (ALE) formulation in a deformable ventricle and includes pressure-driven valves, a 0D Windkessel model for the arterial output and a LVAD boundary condition modeled through a dynamic pressure-flow performance curve. The designed VVUQ plan involves: (a) a risk analysis and the associated credibility goals; (b) a verification stage to ensure correctness in the numerical solution procedure; (c) a sensitivity analysis to quantify the impact of the inputs on the four quantities of interest (QoIs) (average aortic root flow QAoavg , maximum aortic root flow QAomax , average LVAD flow QVADavg , and maximum LVAD flow QVADmax); (d) an uncertainty quantification using six validation experiments that include extreme operating conditions. Results: Numerical code verification tests ensured correctness of the solution procedure and numerical calculation verification showed a grid convergence index (GCI)95% <3.3%. The total Sobol indices obtained during the sensitivity analysis demonstrated that the ejection fraction, the heart rate, and the pump performance curve coefficients are the most impactful inputs for the analysed QoIs. The Minkowski norm is used as validation metric for the uncertainty quantification. It shows that the midpoint cases have more accurate results when compared to the extreme cases. The total computational cost of the simulations was above 100 [core-years] executed in around three weeks time span in Marenostrum IV supercomputer. Conclusions: This work details a novel numerical model for the LV-LVAD system, that is supported by the design and execution of a VVUQ plan created following recognised international standards. We present a methodology demonstrating that stringent VVUQ according to ASME standards is feasible but computationally expensive. Author summary: During the regulatory evaluation of newly developed medical devices, the manufacturer provides proof of the device's safety and effectiveness. Historically, the regulatory entities have accepted bench experiments, animal experiments, and human trials as sources of evidence. But as the research questions become more sophisticated, it is becoming increasingly difficult to find trustworthy answers with the classical approach. Numerical modelling opens a new door for the regulatory process with the promise of tackling these new complex questions. But simulations suffer from a fundamental disconnect with practical applications. While most simulations are deterministic, engineering applications have many sources of uncertainty. Furthermore, the numerical model itself can introduce large uncertainties due to the assumptions and the numerical approximations employed. Without forthrightly estimating the total uncertainty in a prediction, decision makers will be ill advised. Recently published standards such as the ASME V&V40 provides a structured manner to provide credibility evidence for the simulation results. This credibility evidence is supported by a thorough check of the numerical model implementation and a quantitative comparison with a physical experiment. This manuscript shows an end-to-end example for the design and execution of a verification, validation and uncertainty quantification (VVUQ) following the ASME V&V40 standard. [ABSTRACT FROM AUTHOR]