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Many applications involving porous media--notably reservoir engineering and geologic applications--involve tight coupling between multiphase fluid flow, transport, and poromechanical deformation. While numerical models for these processes…
Gravitational waves from neutron-star and black-hole binaries carry valuable information on their physical properties and probe physics inaccessible to the laboratory. Although development of black-hole gravitational-wave templates in the…
Implicit solvers present strong limitations when used on supercomputing facilities and in particular for adaptive mesh-refinement codes. We present a new method for implicit adaptive time-stepping on adaptive mesh refinement-grids. We…
A coupled system of volume integral and hydrodynamic equations is solved to analyze electromagnetic scattering from nanostructures consisting of metallic and dielectric parts. In the metallic part, the hydrodynamic equation relates the free…
We present an immersed interface method for the vorticity-velocity form of the 2D Navier Stokes equations that directly addresses challenges posed by multiply connected domains, nonconvex obstacles, and the calculation of force…
We consider here a cell-centered finite difference approximation of the Richards equation in three dimensions, averaging for interface values the hydraulic conductivity $K=K(p)$, a highly nonlinear function, by arithmetic, upstream, and…
This paper provides primarily an analytical ad hoc -solution for 3-dimensional, incompressible Navier-Stokes equations with a suitable external force field. The solution turns out to be smooth and integrable on the whole space. There is…
Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…
We investigate the long-time behavior of solutions to a stochastically forced one-dimensional Navier-Stokes system, describing the motion of a compressible viscous fluid, in the case of linear pressure law. We prove existence of an…
Constrained least squares problems arise in a variety of applications, and many iterative methods are already available to compute their solutions. This paper proposes a new efficient approach to solve nonnegative linear least squares…
A new computational method is presented to resolve hydrodynamic interactions acting on solid particles immersed in incompressible host fluids. In this method, boundaries between solid particles and host fluids are replaced with a continuous…
Numerical simulations of magneto-convection have greatly expanded our understanding of stellar interiors and stellar magnetism. Recently, fully compressible hydrodynamical simulations of full-star models have demonstrated the feasibility of…
Context. Turbulent convection models in nonlinear radial stellar pulsation models rely on an extra equation for turbulent kinetic energy and fail to adequately explain mode-selection problems. Since multidimensional calculations are…
We develop a $ P $-multigrid solver to simulate locally preconditioned unsteady compressible Navier-Stokes equations at low Mach numbers with implicit high-order methods. Specifically, the high-order flux reconstruction/correction procedure…
We develop a rigid multiblob method for numerically solving the mobility problem for suspensions of passive and active rigid particles of complex shape in Stokes flow in unconfined, partially confined, and fully confined geometries. As in a…
We explore the application of Monte Carlo transport methods to solving coupled radiation-hydrodynamics problems. We use a time-dependent, frequency-dependent, 3-dimensional radiation transport code, that is special relativistic and includes…
Space-time finite-element discretizations are well-developed in many areas of science and engineering, but much work remains within the development of specialized solvers for the resulting linear and nonlinear systems. In this work, we…
We stabilize two-dimensional turbulent Kolmogorov flow by selectively altering the time rate of change of inviscid invariants (energy and enstrophy) of the flow. This method has earlier been demonstrated to modify the two-dimensional…
Current explicit integration techniques in fluid dynamics are deeply limited by the Courant-Friedrichs-Lewy condition of the time step progression, based on the adopted spatial resolution coupled with the maximum value between the kinetic…
In this work, we develop an $\mathcal{O}(N)$ implicit real space method in 1D and 2D for the Cahn Hilliard (CH) and vector Cahn Hilliard (VCH) equations, based on the Method Of Lines Transpose (MOL$^\text{T}$) formulation. This formulation…