A computational framework for pharmaco-mechanical interactions in arterial walls using parallel monolithic domain decomposition methods

A computational framework is presented to numerically simulate the effects of antihypertensive drugs, in particular calcium channel blockers, on the mechanical response of arterial walls. A stretch-dependent smooth muscle model by Uhlmann and Balzani is modified to describe the interaction of pharmacological drugs and the inhibition of smooth muscle activation. The coupled deformation-diffusion problem is then solved using the finite element software FEDDLib and overlapping Schwarz preconditioners from the Trilinos package FROSch. These preconditioners include highly scalable parallel GDSW (generalized Dryja-Smith-Widlund) and RDSW (reduced GDSW) preconditioners. Simulation results show the expected increase in the lumen diameter of an idealized artery due to the drug-induced reduction of smooth muscle contraction, as well as a decrease in the rate of arterial contraction in the presence of calcium channel blockers. Strong and weak parallel scalability of the resulting computational implementation are also analyzed

Parallel Overlapping Schwarz Preconditioners for Incompressible Fluid Flow and Fluid-Structure Interaction Problems

Efficient methods for the approximation of solutions to incompressible fluid flow and fluid-structure interaction problems are presented. In particular, partial differential equations (PDEs) are derived from basic conservation principles. First, the incompressible Navier-Stokes equations for Newtonian fluids are introduced. This is followed by a consideration of solid mechanical problems. Both, the fluid equations and the equation for solid problems are then coupled and a fluid-structure interaction problem is constructed. Furthermore, a discretization by the finite element method for weak formulations of these problems is described. This spatial discretization of variables is followed by a discretization of the remaining time-dependent parts. An implementation of the discretizations and problems in a parallel C++ software environment is described. This implementation is based on the software package Trilinos. The parallel execution of a program is the essence of High Performance Computing (HPC). HPC clusters are, in general, machines with several tens of thousands of cores. The fastest current machine, as of the TOP500 list from November 2019, has over 2.4 million cores, while the largest machine possesses over 10 million cores. To achieve sufficient accuracy of the approximate solutions, a fine spatial discretization must be used. In particular, fine spatial discretizations lead to systems with large sparse matrices that have to be solved. Iterative preconditioned Krylov methods are among the most widely used and efficient solution strategies for these systems. Robust and efficient preconditioners which possess good scaling behavior for a parallel execution on several thousand cores are the main component. In this thesis, the focus is on parallel algebraic preconditioners for fluid and fluid-structure interaction problems. Therefore, monolithic overlapping Schwarz preconditioners for saddle point problems of Stokes and Navier-Stokes problems are presented. Monolithic preconditioners for incompressible fluid flow problems can significantly improve the convergence speed compared to preconditioners based on block factorizations. In order to obtain numerically scalable algorithms, coarse spaces obtained from the Generalized Dryja-Smith-Widlund (GDSW) and the Reduced dimension GDSW (RGDSW) approach are used. These coarse spaces can be constructed in an essentially algebraic way. Numerical results of the parallel implementation are presented for various incompressible fluid flow problems. Good scalability for up to 11 979 MPI ranks, which corresponds to the largest problem configuration fitting on the employed supercomputer, were achieved. A comparison of these monolithic approaches and commonly used block preconditioners with respect to time-to-solution is made. Similarly, the most efficient construction of two-level overlapping Schwarz preconditioners with GDSW and RGDSW coarse spaces for solid problems is reported. These techniques are then combined to efficiently solve fully coupled monolithic fluid-strucuture interaction problems

Implicit large-eddy simulation of compressible flows using the Interior Embedded Discontinuous Galerkin method

We present a high-order implicit large-eddy simulation (ILES) approach for simulating transitional turbulent flows. The approach consists of an Interior Embedded Discontinuous Galerkin (IEDG) method for the discretization of the compressible Navier-Stokes equations and a parallel preconditioned Newton-GMRES solver for the resulting nonlinear system of equations. The IEDG method arises from the marriage of the Embedded Discontinuous Galerkin (EDG) method and the Hybridizable Discontinuous Galerkin (HDG) method. As such, the IEDG method inherits the advantages of both the EDG method and the HDG method to make itself well-suited for turbulence simulations. We propose a minimal residual Newton algorithm for solving the nonlinear system arising from the IEDG discretization of the Navier-Stokes equations. The preconditioned GMRES algorithm is based on a restricted additive Schwarz (RAS) preconditioner in conjunction with a block incomplete LU factorization at the subdomain level. The proposed approach is applied to the ILES of transitional turbulent flows over a NACA 65-(18)10 compressor cascade at Reynolds number 250,000 in both design and off-design conditions. The high-order ILES results show good agreement with a subgrid-scale LES model discretized with a second-order finite volume code while using significantly less degrees of freedom. This work shows that high-order accuracy is key for predicting transitional turbulent flows without a SGS model.Comment: 54th AIAA Aerospace Sciences Meeting, AIAA SciTech, 201

Well-posedness and Robust Preconditioners for the Discretized Fluid-Structure Interaction Systems

In this paper we develop a family of preconditioners for the linear algebraic systems arising from the arbitrary Lagrangian-Eulerian discretization of some fluid-structure interaction models. After the time discretization, we formulate the fluid-structure interaction equations as saddle point problems and prove the uniform well-posedness. Then we discretize the space dimension by finite element methods and prove their uniform well-posedness by two different approaches under appropriate assumptions. The uniform well-posedness makes it possible to design robust preconditioners for the discretized fluid-structure interaction systems. Numerical examples are presented to show the robustness and efficiency of these preconditioners.Comment: 1. Added two preconditioners into the analysis and implementation 2. Rerun all the numerical tests 3. changed title, abstract and corrected lots of typos and inconsistencies 4. added reference

Knowledge-based flow field zoning

Automation flow field zoning in two dimensions is an important step towards easing the three-dimensional grid generation bottleneck in computational fluid dynamics. A knowledge based approach works well, but certain aspects of flow field zoning make the use of such an approach challenging. A knowledge based flow field zoner, called EZGrid, was implemented and tested on representative two-dimensional aerodynamic configurations. Results are shown which illustrate the way in which EZGrid incorporates the effects of physics, shape description, position, and user bias in a flow field zoning

Proceedings for the ICASE Workshop on Heterogeneous Boundary Conditions

Domain Decomposition is a complex problem with many interesting aspects. The choice of decomposition can be made based on many different criteria, and the choice of interface of internal boundary conditions are numerous. The various regions under study may have different dynamical balances, indicating that different physical processes are dominating the flow in these regions. This conference was called in recognition of the need to more clearly define the nature of these complex problems. This proceedings is a collection of the presentations and the discussion groups