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A reconstructed direct discontinuous Galerkin method is developed and evaluated for simulating the compressible laminar and turbulent flows on hybrid grids. The spatial discretization is implemented through the combination of a highly efficient high-order hybrid reconstructed discontinuous Galerkin method together with a newly developed direct discontinuous Galerkin method for computing viscous fluxes. A variety of typical test cases are selected to evaluate the performance of the proposed hybrid reconstructed direct discontinuous Galerkin method for simulating both laminar flows and turbulent flows. Compared with the traditional discontinuous Galerkin method, the hybrid reconstructed direct discontinuous Galerkin method demonstrates its superior potential of being more accurate and more efficient under the same number of degrees of freedom, thus, shows its promise for further practical applications. [ABSTRACT FROM AUTHOR]

An upwind finite volume method on curvilinear grids has been developed to simulate two-dimensional, inviscid, incompressible free surface flows. In this method, the level set method is used to capture the interface. The level set equation and the flow governing equations (Euler equations) are not solved separately, but incorporated into a system equation. The artificial compressibility method is adopted to solve the resulting hyperbolic equations. The MUSCL-Roe scheme, which is widely used in compressible flow computations, is employed to discretize the convective terms. A fully implicit dual-time stepping method with a highly efficient LU-SSOR algorithm as sub-iteration scheme is applied to advance the solution in time. In the present study, a re-initialization method on curvilinear grids for level set function is presented. An example of re-initialization for level set function on curvilinear grids is demonstrated and the resulting level set function is in good agreement with the exact distance function. Numerical results of a sloshing tank problem and a broken dam problem agree well with the theoretical and experimental data, respectively. The free surface flow over a submerged hydrofoil is also simulated using overset grids to demonstrate the capability of dealing with complex geometry. At last, the simulation of droplet splash problem is performed to show the ability of the present method in handling topological changes of the free surface. [ABSTRACT FROM AUTHOR]