An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

Compact high order finite volume method on unstructured grids III: Variational reconstruction

Parametric study on mixing augmentation mechanism induced by cantilevered ramp injectors in a shock-induced combustion ramjet engine

A reconstruction-based discontinuous Galerkin method is presented for the solution of the compressible Navier-Stokes equations on arbitrary grids. In this method, an in-cell reconstruction is used to obtain a higher-order polynomial representation of the underlying discontinuous Galerkin polynomial solution and an inter-cell reconstruction is used to obtain a continuous polynomial solution on the union of two neighboring, interface-sharing cells. The in-cell reconstruction is designed to enhance the accuracy of the discontinuous Galerkin method by increasing the order of the underlying polynomial solution. The inter-cell reconstruction is devised to remove an interface discontinuity of the solution and its derivatives and thus to provide a simple, accurate, consistent, and robust approximation to the viscous and heat fluxes in the Navier-Stokes equations. A parallel strategy is also devised for the resulting reconstruction discontinuous Galerkin method, which is based on domain partitioning and Single Program Multiple Data (SPMD) parallel programming model. The RDG method is used to compute a variety of compressible flow problems on arbitrary meshes to demonstrate its accuracy, efficiency, robustness, and versatility. The numerical results demonstrate that this RDG method is third-order accurate at a cost slightly higher than its underlying second-order DG method, at the same time providing a bettermore » performance than the third order DG method, in terms of both computing costs and storage requirements.« less

A Parallel Reconstructed Discontinuous Galerkin Method for the Compressible Flows on Aritrary Grids

Interface-preserving level set method for simulating dam-break flows

The direct Discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids

A direct discontinuous Galerkin method for the compressible NavierStokes equations on arbitrary grids

An upwind finite volume method for incompressible inviscid free surface flows

The relationship between the number of detonation waves and the evolution process of the flow field in a rotating detonation engine was investigated through a numerical analysis. The simulations were based on the Euler equation and a detailed chemical reaction model. In the given engine model, the flow-field evolution became unstable when a single detonation wave was released. New detonation waves formed spontaneously, changing the operational mode from single-wave to four-wave. However, when two or three detonation waves were released, the flow field evolved in a quasi-steady manner. Further study revealed that the newly formed detonation wave resulted from an accelerated chemical reaction on the contact surface between the detonation products and the reactive mixture. To satisfy the stable propagation requirements of detonation waves, we proposed a parameter called NL, which can be compared with the number of detonation waves in the combustor to predict the evolution (quasi-stable or unstable) of the flow field. Finally, we verified the effectiveness of NL in a redesigned engine. This study may assist the operational mode control in rotating detonation engine experiments.

Xiaoquan Yang

Papers

The direct Discontinuous Galerkin method for the compressible Navier-Stokes equations on arbitrary grids

A direct discontinuous Galerkin method for the compressible NavierStokes equations on arbitrary grids

An upwind finite volume method for incompressible inviscid free surface flows

Operational mode transition in a rotating detonation engine

A reconstructed direct discontinuous Galerkin method for simulating the compressible laminar and turbulent flows on hybrid grids