Coupled continuous quadratic knapsack problems (CCK) are introduced in the present study. The solution of a CCK problem is equivalent to the projection of an arbitrary point onto the volume constrained Gibbs N-simplex, which has a wide range of applications in computational science and engineering. Three algorithms have been developed in the present study to solve large scale CCK problems. According to the numerical experiments of this study, the computational costs of presented algorithms scale linearly with the problem size, when it is sufficiently large. Moreover, they show competitive or even superior computational performance compared to the advanced QP solvers. The ease of implementation and linear scaling of memory usage with the problem size are the other benefits of the presented algorithms.