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In this work, we propose a novel strategy for the numerical solution oflinear convection diffusion equation (CDE) over unfitted domains. In theproposed numerical scheme, strategies from high order Hybridized DiscontinuousGalerkin method and eXtended Finite Element method is combined with the levelset definition of the boundaries. The proposed scheme and hence, is named aseXtended Hybridizable Discontinuous Galerkin (XHDG) method. In this regard, theHybridizable Discontinuous Galerkin (HDG) method is eXtended to the unfitteddomains; i.e, the computational mesh does not need to fit to the domainboundary; instead, the boundary is defined by a level set function and cutsthrough the background mesh arbitrarily. The original unknown structure of HDGand its hybrid nature ensuring the local conservation of fluxes is kept, whiledeveloping a modified bilinear form for the elements cut by the boundary. Atevery cut element, an auxiliary nodal trace variable on the boundary isintroduced, which is eliminated afterwards while imposing the boundaryconditions. Both stationary and time dependent CDEs are studied over a range offlow regimes from diffusion to convection dominated; using high order $(p \leq4)$ XHDG through benchmark numerical examples over arbitrary unfitted domains.Results proved that XHDG inherits optimal $(p + 1)$ and super $(p + 2)$convergence properties of HDG while removing the fitting mesh restriction.

eXtended Hybridizable Discontinous Galerkin (X-HDG) Method for Linear Convection-Diffusion Equations on Unfitted Domains