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PyLith, a community, open-source code for modelling quasi-static and dynamic crustal deformation with an emphasis on earthquake faulting, has recently been updated with a flexible multiphysics implementation. We demonstrate the versatility of the multiphysics implementation by extending the code to model fully coupled continuum poromechanics. We verify the newly incorporated physics using standard benchmarks for a porous medium saturated with a slightly compressible fluid. The benchmarks include the 1-D consolidation problem as outlined by Terzaghi, Mandel’s problem for the 2-D case, and Cryer’s problem for the 3-D case. All three benchmarks have been added to the PyLith continuous integration test suite. We compare the closed form analytical solution for each benchmark against solutions generated by our updated code, and lastly, demonstrate that the poroelastic material formulation may be used alongside the existing fault implementation in PyLith.

 

We present a study of the standard plasma physics test, Landau damping, using the Particle-In-Cell (PIC) algorithm. The Landau damping phenomenon consists of the damping of small oscillations in plasmas without collisions. In the PIC method, a hybrid discretization is constructed with a grid of finitely supported basis functions to represent the electric, magnetic and/or gravitational fields, and a distribution of delta functions to represent the particle field. Approximations to the dispersion relation are found to be inadequate in accurately calculating values for the electric field frequency and damping rate when parameters of the physical system, such as the plasma frequency or thermal velocity, are varied. We present a full derivation and numerical solution for the dispersion relation, and verify the PETSC-PIC numerical solutions to the Vlasov-Poisson for a large range of wave numbers and charge densities. 

Paraffin wax is a prominent solid fuel for hybrid rockets. The atomization process of the paraffin wax fuel into he hybrid rocket combustion involves the droplets pinching off from the fuel surface. Therefore, droplet formation and pinch-off dynam- ics is analyzed using a one-dimensional axisymmetric approximation to understand droplet size distribution and pinch-off time. A mixed finite element formulation is used to solve the numerical problem. The computational algorithm uses adaptive mesh refinement to capture singularity and runs self-consistently to calculate droplet elongation. The code is verified using the Method of Manufactured Solution (MMS) and validated against laboratory experiments. Moreover, paraffin wax simulations are explored for varying inlet radius and it is found that the droplet size increases very slightly with the increasing inlet radius. Also, the pinch-off time increases up to a point where it starts to decrease as we increase the inlet radius. This behavior leads to a conjecture for the theoretical maximum radius that the droplet approaches as the inlet radius increases, which is a motivation for the future work. 

Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinch-off happens. A one-dimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the self-similar nature of the solution. Numerical models for the one-dimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a one-dimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for one-dimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinch-off phenomena. 

Effective relaxation methods are necessary for good multigrid convergence. For many equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated space decompositions are required; examples include problems with semidefinite terms or saddle point structure. In this article, we present a unifying software abstraction, PCPATCH, for the topological construction of space decompositions for multigrid relaxation methods. Space decompositions are specified by collecting topological entities in a mesh (such as all vertices or faces) and applying a construction rule (such as taking all degrees of freedom in the cells around each entity). The software is implemented in PETSc and facilitates the elegant expression of a wide range of schemes merely by varying solver options at runtime. In turn, this allows for the very rapid development of fast solvers for difficult problems. 

Edema, also termed oedema, is a generalized medical condition associated with an abnormal aggregation of fluid in a tissue matrix. In the intestine, excessive edema can lead to serious health complications associated with reduced motility. A $7.5\%$ solution of hypertonic saline (HS) has been hypothesized as an effective means to reduce the effects of edema following surgery or injury. However, detailed clinical edema experiments can be difficult to implement, or costly, in practice. In this manuscript we introduce an implicit in time discontinuous Galerkin method with novel adaptations for modeling edema in the 3D layered physiology of the intestine. The model improves over early work via inclusion of the tissue intrinsic storage coefficient, and the effects of Starling overestimation for high venous pressures. Validation against a recent clinical experiment in HS resuscitation of acute edema is presented; the results support the clinical hypothesis that 7.5% HS solution may be effective in the resuscitation of acute edema formation. New results include an improved view into the effects of resuscitation on the hydrostatic pressure profile of edematous rats, effects on lumenal volume attenuation, relative fluid gain and an estimation of the impacts of both acute edema and resuscitation on intestinal motility.

 

We demonstrate that the solvation‐layer interface condition (SLIC) continuum dielectric model for molecular electrostatics, combined with a simple solvent‐accessible‐surface‐area (SASA)‐proportional model for nonpolar solvent effects, accurately predicts solvation entropies of neutral and charged small molecules. The SLIC/SASA model has only seven fitting parameters in total and achieves this accuracy using a training set with only 20 compounds. Despite this simplicity, solvation free energies and entropies are nearly as accurate as those predicted by the more sophisticated Langevin dipoles solvation model. Surprisingly, the model automatically reproduces the negligible contribution of electrostatics to the solvation of hydrophobic compounds. Opportunities for improvement include nonpolar solvation, anion solvation entropies, and heat capacities. More molecular realism may be needed for these quantities. To enable a future, explicit‐solvent‐based assessment of the SLIC/SASA implicit‐solvent model, we predict solvation entropies for the Mobley test set, which are available as Supporting Information.

 

Pipelined Krylov methods seek to ameliorate the latency due to inner products necessary for projection by overlapping it with the computation associated with sparse matrix‐vector multiplication. We clarify a folk theorem that this can only result in a speedup of 2× over the naive implementation. Examining many repeated runs, we show that stochastic noise also contributes to the latency, and we model this using an analytical probability distribution. Our analysis shows that speedups greater than 2× are possible with these algorithms. Copyright © 2016 John Wiley & Sons, Ltd.