Dartzi Pan

Upwind finite-volume Navier-Stokes computations on unstructured triangular meshes

A Navier-Stokes solver using upwind finite-volume method on unstructured triangular meshes is developed and tested. A Godunov-type upwind method is used for inviscid flux computations. An accurate linear reconstruction is used to compute the two Riemann states at the cell face, and Roes approximate Riemann solver is solved for inviscid fluxes. A finite-volume formulation for the viscous terms, which can be second-order accurate for a large clans of triangular cells, is developed and tested. The algebraic Baldwin-Lomax turbulence model is implemented via the use of a turbulence reference grid, the only purpose of which is to provide nessesary length scales to the model

An Immersed Boundary Method on Unstructured Cartesian Meshes for Incompressible Flows with Heat Transfer

ABSTRACT The incompressible Navier–Stokes equations with heat transfer are solved by an implicit pressure-correction method on unstructured Cartesian meshes. An immersed boundary method is also implemented to treat arbitrary solid bodies in the flow field. The domain occupied by the immersed bodies is viewed as being occupied by the same fluid as outside, with a prescribed velocity and temperature field. With this view, the pressure inside the immersed bodies satisfies the same pressure Poisson equation as outside. Multigrid methods are developed to solve the difference equations for pressure, velocity, and temperature field. Various forced-convection and natural-convection test problems are computed to validate the present methodology.

A new approximate LU factorization scheme for the Reynolds-averaged Navier-Stokes equations

A new approximate LU factorization scheme is developed to solve the steady-state Reynolds-averaged NavierStokes (NS) equations. Central differencing is used for both implicit and explicit operators, and special care is taken to obtain well-conditioned factors on the implicit side. The scheme is then analyzed and optimized according to a simple linear analysis. It is unconditionally stable for the model hyperbolic equation in both two and three dimensions. However, the requirement for well-conditioned factors has essentially limited the effective time step that the scheme can achieve. Supersonic and transonic 3-D flows past a hemisphere cylinder are computed to demonstrate the convergence characterstics of the scheme. A good convergence rate is achieved in the inviscid case. Finally, an explicit eigenvector annihilation procedure is employed successfully to remove the stiffness caused by the fine grid spacing for viscous flows.

Transonic flutter suppression using active acoustic excitations

The objective of this work is to study the feasibility of using acoustic waves as a means for suppressing the flutter instability of a typical section in transonic flow. A high-resolution upwind TVD flow solver of acoustic accuracy was first constructed and validated on a dynamic mesh system. The geometric conservation law was implemented consistently with the physical conservation law via a suitably defined cell boundary speed. This specially developed structure/fluid/acoustic solver was then integrated in the time domain to study whether flutter can be suppressed using active acoustic excitations. Flutter suppression was achieved in the transonic region when an appropriate feedback control law was used. Large-amplitude limit cycle type oscillation in a transonic flow was also simulated. It was found that the present acoustic control technique can only be effective when the amplitude of the oscillation is small in accordance with previous findings obtained in a low-speed wind-tunnel test.

A General Boundary Condition Treatment in Immersed Boundary Methods for Incompressible Navier-Stokes Equations with Heat Transfer

A general boundary condition scheme for incompressible flows over immersed bodies on Cartesian grids is developed to treat Dirichlet, Neumann, and Robin boundary conditions on the immersed surfaces. Various forced and natural convection problems over a circular cylinder and the nature convection between two concentric cylinders are computed to validate the proposed scheme. Results show that the method is second-order in L 1 and L 2 norms for velocity, pressure, and temperature for all three boundary conditions. The method is also second-order in L∞ norm for Dirichlet boundary condition, while it is of the order of 1.4 in L∞ norm when Neumann or Robin condition is applied.

A simple and accurate ghost cell method for the computation of incompressible flows over immersed bodies with heat transfer

A simple, stable, and accurate ghost cell method is developed to solve the incompressible flows over immersed bodies with heat transfer. A two-point stencil is used to build the flow reconstruction models for both Dirichlet and Neumann boundary conditions on the immersed surface. Tests show that the current scheme is second-order-accurate in all error norms for both types of boundary condition, with the only exception that under Neumann condition the order of the maximum norm of temperature error is 1.44. Various forced- and natural-convection problems for cylinders immersed in open field or in a cavity are computed and compared with published data.

INCOMPRESSIBLE FLOW SOLUTION ON UNSTRUCTURED TRIANGULAR MESHES

Abstract An incompressible Navier-Stokes solver on unstructured triangular mesh is developed and tested. The artificial compressibility method is employed to render the system hyperbolic. The temperature equation and the source terms representing thermal buoyancy forces art included in the system via Boussinesq approximation. A Godunov-type second-order upwind finite-volume method is used to obtain inviscid fluxes. The viscous terms art computed by a finite-volume formulation which can be second-order accurate for a large class of triangular cells. To maintain numerical stability and efficiency, an implicit approximate LU factorization (ALU) scheme is used for time integration. Time accuracy is assured by subilerations at each time step. Various forced-convection and natural-convection problems art computed to validate the proposed scheme.

Computation of internal flow with free surfaces using artificial compressibility

In this article an upwind flux-differencing scheme using artificial compressibility is generalized to allow time-accurate computation of incompressible flows on a dynamic grid system. By treating the free surface as a moving grid line that connects in a Lagrangian fashion, the scheme can be applied to solve a variety of free surface flows of moderate surface deformation. The surface tension effects can also be included using a source term and via boundary condition.

Upwind finite-volume method for natural and forced convection

A third-order upwind finite-volume method was applied to solve the incompressible Navier-Stokes equations via the use of artificial compressibility. The energy equation and the source terms representing thermal buoyancy are included in the system. The inviscid fluxes are evaluated by a MUSCL-type flux difference upwind scheme based on the inviscid eigensystem. An implicit, approximate factorization (AF) scheme was used for time integration, and subiterations at each time step can be applied to obtain time accuracy. Various steady and unsteady tests are performed to validate the present method, including problems in natural convection and forced convection, and in particular the complex flow field over two circular cylinders displaced normally to free stream.

Numerical simulation of trailing-edge acoustic/vortical interaction

The objective or the present research is twofold. The first part concerns the construction or a high-resolution aeroacoustic flow solver, and the remaining emphasizes the wave/vortex interaction around a sharp trailing edge. Euler equations and the Osher-Chakravarthy MUSCL-type high-resolution upwind TVD scheme were used, respectively, as the flow model and the numerical algorithm to analyze the acoustically excited flow. Modification on the reconstruction of the cell interface values was first made to improve the scheme fidelity so that a wave propagationproblem can be solved on nonuniform mesh systems. An acoustic source modeling was also devised to simulate the generation of sound emitted from a monopole located on the solid boundary. The numerical algorithm was first evaluated by checking the computed results with several test problems that have analytic solutions. Results show that the currently proposed computational aeroacoustic scheme is accurate and reliable. An acoustically excited incompressible and low-Mach-number flow over a finite plate was then simulated. The results show that the unsteady airloads induced by acoustic/vortical interaction around a sharp trailing edge can be satisfactorily resolved by the currently developed inviscid Euler flow solver