Motivation
and objectives
The Joe code is a
2nd-order accurate (in space), finite volume, unstructured cell-based, implicit
RANS (Reynolds-averaged Navier-Stokes equations) solver with flamelet-based chemistry
(Pecnik et al. 2010a,b) developed within the Stanford PSAAP Center. This code
was created to simulate the flow path inside of scramjet engines and, during
the past few years, has served as the platform for numerical simulations on complex
multiphysics problems. However, some robustness and computational cost aspects
of the original code were not sufficiently fine-tuned, and, therefore, the
improvement of these aspects has motivated the present research.
At the beginning of
2011, Joe included the following numerical methods for solving the RANS
equations: space integration using a HLLC (Harten, Lax, van Leer contact wave)
approximate nonlinear Riemann solver (Toro et al. 1994), 2nd-order
extrapolation of the convective terms using a MUSCL scheme (Monotone
Upstream-centered Schemes for Conservation Laws), and 2nd-order space
integration of the viscous terms. Steadystate time integration could be carried
out using a multistage Runge-Kutta scheme or a backward Euler method where the
linear system is solved using preconditioned GMRES (Generalized Minimum
RESidual) or a BiCGSTAB (BiConjugate Gradient STABilized) method.
Using these numerical
methods, and when convergence is reached, the Joe solver results in accurate
simulations. However, several issues present robustness challenges and prevent the
application of the software to full 3D geometry UQ (Uncertainty Quantification)
studies. It is important to note that UQ studies using the complete 3D Hyshot
II geometry are an important milestone of the PSAAP center and, for that
reason, significant effort has been devoted to increasing the robustness and
convergence rates of the solver. In particular, during this past year, the
following numerical methods have been added to the baseline Joe solver:
• New numerical
discretization of the convective terms: both the AUSM (Advection
Upstream Splitting
Method) approximate nonlinear Riemann solver (Liou & Steffen
1993) and a JST
(Jameson -Schmidt-Turkel) centered scheme (Jameson et al. 1981).
• A geometric,
agglomeration-basedmultigrid scheme implemented and tuned for flows
with shocks.
• New linear solvers:
BiCGSTAB with linelet preconditioning and a LU-SGS (LU
Symmetric Gauss Seidel)
method.
• New estimation of the
local time stepping for viscous and turbulent flows to enable
larger CFL numbers.
The objective of this
paper is to briefly introduce the new methods that have been implemented in Joe
and to show the numerical improvements (robustness, and speed) that those
techniques have produced. The overall goal has been to enable the 3D UQ simulations
that the Center needs to pursue during the coming year.
Authors:
F. Palacios/J.J. Alonso Source:http://ctr.stanford.edu/ResBriefs/2011/26_palacios.pdf
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