@article{pandare_luo_2018, title={A robust and efficient finite volume method for compressible inviscid and viscous two-phase flows}, volume={371}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2018.05.018}, abstractNote={A robust and efficient density-based finite volume method is developed for solving the six-equation single pressure system of two-phase flows at all speeds on hybrid unstructured grids. Unlike conventional approaches where an expensive exact Riemann solver is normally required for computing numerical fluxes at the two-phase interfaces in addition to AUSM-type fluxes for single-phase interfaces in order to maintain stability and robustness in cases involving interactions of strong pressure and void-fraction discontinuities, a volume-fraction coupling term for the AUSM+-up fluxes is introduced in this work to impart the required robustness without the need of the exact Riemann solver. The resulting method is significantly less expensive in regions where otherwise the Riemann solver would be invoked. A transformation from conservative variables to primitive variables is presented and the primitive variables are then solved in the implicit method in order for the current finite volume method to be able to solve, effectively and efficiently, low Mach number flows in traditional multiphase applications, which otherwise is a great challenge for the standard density-based algorithms. A number of benchmark test cases are presented to assess the performance and robustness of the developed finite volume method for both inviscid and viscous two-phase flow problems. The numerical results indicate that the current density-based method provides an attractive and viable alternative to its pressure-based counterpart for compressible two-phase flows at all speeds.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Pandare, Aditya K. and Luo, Hong}, year={2018}, month={Oct}, pages={67–91} }
 @article{pandare_luo_bakosi_2019, title={An enhanced AUSM(+)-up scheme for high-speed compressible two-phase flows on hybrid grids}, volume={29}, ISSN={["1432-2153"]}, DOI={10.1007/s00193-018-0861-x}, abstractNote={An enhanced $$\hbox {AUSM}^+$$ -up scheme is presented for high-speed compressible two-phase flows using a six-equation two-fluid single-pressure model. Based on the observation that the $$\hbox {AUSM}^+$$ -up flux function does not take into account relative velocity between the two phases and thus is not stable and robust for computation of two-phase flows involving interaction of strong shock waves and material interfaces, the enhancement is in the form of a volume fraction coupling term and a modification of the velocity diffusion term, both proportional to the relative velocity between the two phases. These modifications in the flux function obviate the need to employ the exact Riemann solver, leading to a significantly less expensive yet robust flux scheme. Furthermore, the Tangent of Hyperbola for INterface Capturing (THINC) scheme is used in order to provide a sharp resolution for material interfaces. A number of benchmark test cases are presented to assess the performance and robustness of the enhanced $$\hbox {AUSM}^+$$ -up scheme for compressible two-phase flows on hybrid unstructured grids. The numerical experiments demonstrate that the enhanced $$\hbox {AUSM}^+$$ -up scheme along with THINC scheme can efficiently compute high-speed two-fluid flows such as shock–bubble interactions, while accurately capturing material interfaces.}, number={5}, journal={SHOCK WAVES}, author={Pandare, A. K. and Luo, H. and Bakosi, J.}, year={2019}, month={Jul}, pages={629–649} }
 @article{pandare_luo_2016, title={A hybrid reconstructed discontinuous Galerkin and continuous Galerkin finite element method for incompressible flows on unstructured grids}, volume={322}, ISSN={["1090-2716"]}, DOI={10.1016/j.jcp.2016.07.002}, abstractNote={A hybrid reconstructed discontinuous Galerkin and continuous Galerkin method based on an incremental pressure projection formulation, termed rDG ( P n P m ) + CG ( P n ) in this paper, is developed for solving the unsteady incompressible Navier–Stokes equations on unstructured grids. In this method, a reconstructed discontinuous Galerkin method ( rDG ( P n P m ) ) is used to discretize the velocity and a standard continuous Galerkin method ( CG ( P n ) ) is used to approximate the pressure. The rDG ( P n P m ) + CG ( P n ) method is designed to increase the accuracy of the hybrid DG ( P n ) + CG ( P n ) method and yet still satisfy Ladyženskaja–Babuška–Brezzi (LBB) condition, thus avoiding the pressure checkerboard instability. An upwind method is used to discretize the nonlinear convective fluxes in the momentum equations in order to suppress spurious oscillations in the velocity field. A number of incompressible flow problems for a variety of flow conditions are computed to numerically assess the spatial order of convergence of the rDG ( P n P m ) + CG ( P n ) method. The numerical experiments indicate that both rDG ( P 0 P 1 ) + CG ( P 1 ) and rDG ( P 1 P 2 ) + CG ( P 1 ) methods can attain the designed 2nd order and 3rd order accuracy in space for the velocity respectively. Moreover, the 3rd order rDG ( P 1 P 2 ) + CG ( P 1 ) method significantly outperforms its 2nd order rDG ( P 0 P 1 ) + CG ( P 1 ) and rDG ( P 1 P 1 ) + CG ( P 1 ) counterparts: being able to not only increase the accuracy of the velocity by one order but also improve the accuracy of the pressure.}, journal={JOURNAL OF COMPUTATIONAL PHYSICS}, author={Pandare, Aditya K. and Luo, Hong}, year={2016}, month={Oct}, pages={491–510} }