Interest in operational cost reduction is driving engine manufacturers to consider low-cost fuel substitution in heavy-duty diesel engines. These dual-fuel (DF) engines could be operated either in diesel-only mode or operated with premixed natural gas (NG) ignited by a pilot flame of compression-ignited direct-injected diesel fuel. Under certain conditions, dual-fuel operation can result in increased cycle-to-cycle variability (CCV) during combustion. CFD can greatly help in understanding and identifying critical parameters influencing CCV. Innovative modelling techniques and large computing resources are needed to investigate the factors affecting CCV in dual-fuel engines. This paper discusses the use of the High Performance Computing resource Titan, at Oak Ridge National Laboratory, to investigate CCV of a dual-fuel engine. The CONVERGE CFD software was used to simulate multiple, parallel single cycles of dual-fuel combustion with perturbed operating parameters and boundary conditions. Perturbations associated with a single parameter can be studied using samples distributed according to a one dimensional interpolation rule. However, extending such techniques to a multidimensional context is a challenge since the straight forward tensorization leads to an exponential growth of the required number of samples. In contrast, sparse grids are constructed from a linear combination of tensors with varying degree in each dimension where the tensors are chosen in a way that leads to a stable surface fitting algorithm of arbitrary order of accuracy with minimal number of samples. This technique is expected to be useful to understand and predict combustion stability limits in dual fuel combustion.