Adaptive grid computation for inviscid compressible flows using a pressure correction method

Abstract

Effort has been devoted to extending a pressure correction based incompressible flow algorithm developed earlier to calculate compressible flows. The resulting algorithm represents a substantial generalization of the original algorithm, retaining the same basic structure (curvilinear coordinates, staggered grid, pressure correction method, no artificial smoothing terms) and capabilities of the original scheme while adding the new capabilities. With the inclusion of the density variation effects, the pressure correction equation now becomes a convection-diffusion type of transport equation, instead of being a difision type of equation as it is for incompressible cases. The convection effects are dominant for high Mach number flow, and can affect the stability of the low Mach number flow computation. Appropriate numerical treatments are necessary to account for this change of characteristics of the pressure correction equation. The modified pressure correction equation also requires a change of the boundary conditions for pressure between subsonic and supersonic flows. By combining the revised algorithm and an adaptive grid procedure developed earlier, accurate inviscid flow solutions over a wide range of Mach numbers can now be successfully obtained. Several different flow problems, ranging from subsonic and transonic to hypersonic, have been computed to demonstrate the performance of the new algorithm.

A Unified Method for Computing Incompressible and Compressible Flows in Boundary-Fitted Coordinates

“…A staggered grid was first used to compute compressible flows by Harlow and Amsden [10,11], generalizing the MAC scheme of Harlow and Welch [12] to the compressible case, in orthogonal coordinates. Later works in this direction, using general coordinates, are [17,18,20,36,38,39]. This is also the approach taken by us here.…”

“…This will, therefore, not be explained, and we will only show results obtained for the Navier-Stokes equations. Compared to the earlier work quoted above, we unify the following two existing methodologies, combining their advantages: (a) a nondimensionalization similar to that of Shuen et al [36] that eliminates the singularity associated with M ↓ 0; (b) a general coordinate version of the staggered grid method of Harlow and Amsden [10,11], similar to that of Shyy [38,39].…”

A Pressure-Based Method for Turbulent Cavitating Flow Computations

“…In the pressure-based algorithm, the pressure-correction equation has been revised to achieve successful solutions for highly compressible flows [23,31,32]. We will describe this formulation in the context of noncavitating flows with compressibility effects to motivate the present cavitating flow method.…”

“…Another aspect is that, similar to compressible flow computations, the density at the cell face is upwinded both in the discretized momentum and pressure-correction equations [23,26,31]. The criterion for upwinding is based on the value of liquid volume fraction; that is, wherever α l is less than 1.0, the cell-faced density value is estimated based on an upwinded formula.…”

Computational mechanics

“…One of the main concerns in CFD world is the computational cost of the algorithms and solvers. Better solution algorithms [30,31,32], solvers [33,34], and multigrid techniques [35,36,37,38] have lowered the computational cost and brought the feasible solutions to real life fluid flow problems. Over the past decades the work on pressure-2 based algorithms [4,6,7,12,30,31,32,36], extended the techniques to solve flow problems in various Reynolds and Mach number regimes using both structured and unstructured grid methods.…”