Interior Penalty Schemes for Discontinuous Isogeometric Methods With an Application to Nuclear Reactor Physics

Until recently, interior penalty methods have been applied to elliptic operators using an approach based on the mass matrix of finite elements that possess a constant Jacobian. In the case of isogeometric analysis, such an approach would not always guarantee coercivity of the bilinear form and thus numerical stability of the solution. In this paper, optimal interior penalty parameters [1] are described and applied to the symmetric interior penalty scheme of the discontinuous Galerkin isogeometric spatial discretisation of the neutron diffusion equation. The numerical accuracy of the proposed method is compared against a standard continuous Bubnov-Galerkin isogeometric spatial discretisation of the neutron diffusion equation. Numerical consistency and order of error-convergence is verified by means of the method of manufactured solutions. Numerical results are also presented for a two-dimensional pin-cell test case, based upon the OECD/NEA C5G7 quarter core MOX fuel assembly benchmark for nuclear reactor physics parameters of interest.