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A variational positivity-persevering stabilization scheme is proposed to solve the Spalart-Allmaras (S-A) turbulence model
employed in Detached Eddy Simulation (DES) modeling for fluid-structure interaction at high Reynolds number. The S-A
model equation has the eects of convection, diusion as well as reaction. Moreover, the reactive term can change signs
pertaining to production or destruction phenomenon in the modeled turbulence eects. The stabilization relies on a mixed
form the Galerkin/Least Squares (GLS) - Sub-Grid Scale (SGS) while maintaining the positivity-preserving property of
solution field. The motivation behind this investigation arises from the modeling of vortex-induced vibration (VIV) in
deep-water drilling risers. The ocean current in deep-waters can reach up to high Reynolds number of the order 105 􀀀 106
which can lead to higher bending stress and fatigue failure of riser system. Our ultimate aim is to predict the eect of the
VIV on the riser system connected with drill ship undergoing surge and heave movement in harsh deepwater environment.
For such coupled systems, we need a robust turbulence model to analyze fluid-structure interaction. Since both Direct
Numerical Simulation (DNS) and Large Eddy Simulation (LES) are beyond the capacity of current computer hardware for
high Reynolds number and Unsteady RANS (URANS) is not reliable for massively separated vortex flows, we consider
Detached Eddy Simulation (DES) formulation for the coupled analysis of oshore riser system. The underlying S-A
equation of DES is phenomenological and several numerical challenges are faced while dealing with it, namely (a) the
inclusion of the reactive terms, (b) the production and destruction eects, and (c) spurious oscillations near the boundary
and internal layers. Conventional stabilization methods mainly focus on the stability of convection dominated flows, but
hardly take into account the reaction-dominated flows. Several stabilization methods have been proposed to stabilize
the convection-diusion-reaction equation based on the Streamline Upwind Petrov-Galerkin and Galerkin-Least Squares
method, but they fail to stabilize the solution when the reaction coecient becomes negative. However, the Sub-Grid
Scale method oers a solution to this issue but the solution is highly diusive for certain positive reactive coecients
and boundary conditions. Hence, we propose a combination of these two methods which behaves as GLS in the positive
reaction coecient regime and as an SGS method pertaining to negative reaction coecient.
In this work, our strategy is to employ the Discrete Upwind algebraic operator to maintain positivity in the solution at the
element level matrix. This guarantees that the numerical solution does not manifest spurious oscillations near the internal
as well as boundary layers, which allows to cover all the possible regimes of the canonical equation while maintaining the
monotonicity property. Error analysis in one dimension showed reduced L2 error for the proposed method with varying
non-dimensional numbers based on the equation considered - Da = sl=u for convection-reaction equation, ! = sl2=k for
diusion-reaction equation and Pe = ul=2k for convection-diusion equation, with u, k, s, l being the advection velocity,
diusion coecient, reaction coecient and element length, respectively. We employ the proposed idea to the DES for
demonstrating the eectiveness of the method for partitioned iterative fluid-structure solver [1, 2].