Efficient projection kernels for discontinuous Galerkin simulations of disperse multiphase flows on arbitrary curved elements

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In this work, we develop projection kernels for Euler-Lagrange point-particle simulations of disperse multiphase flows on arbitrary curved elements. These kernels are employed in a high-order discontinuous Galerkin framework for projecting the action of the particles to the Eulerian mesh. Instead of commonly used isotropic kernels, such as a Gaussian-type kernel, we construct an anisotropic polynomial-based smoothing function that preserves the compactness of the discontinuous Galerkin method on high-aspect-ratio elements and maintains an acceptable computational cost. At the same time, it mitigates inaccuracies associated with larger particles and numerical instabilities arising from the Dirac delta function and low-order kernels. Specifically, the geometric mapping of a physical element to the reference element is exploited to construct a kernel that is elliptical in 2D and ellipsoidal in 3D. We also develop a strategy to conserve interphase transfer near boundaries, particularly on curved elements. This strategy employs a high-order polynomial approximation to appropriately rescale the interphase source terms in an efficient manner. The compatibility of the proposed methodology with different types of meshes is investigated. We then apply it to a number of particle-laden flow configurations, including supersonic dusty flow over a flat plate, moving shocks interacting with clouds of particles, and hypersonic dusty flows over blunt bodies.