Jeffrey W. Banks

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A numerical method is described for inviscid, compressible, multi-material flow in two space dimensions. The flow is governed by the multi-material Euler equations with a general mixture equation of state. Composite overlapping grids are used to handle complex flow geometry and block-structured adaptive mesh refinement (AMR) is used to locally increase grid(More)
This paper explores the development of a scalable, nonlinear, fully-implicit stabilized unstructured finite element (FE) capability for 2D incompressible (reduced) resistive MHD. The discussion considers the implementation of a stabilized FE formulation in context of a fully-implicit time integration and direct-to-steady-state solution capability. The(More)
A common attribute of capturing schemes used to find approximate solutions to the Euler equations is a sub-linear rate of convergence with respect to mesh resolution. Purely nonlinear jumps, such as shock waves produce a first-order convergence rate, but linearly degenerate discontinuous waves, where present, produce sub-linear convergence rates which(More)
In multi physics computations where a compressible fluid is coupled with a linearly elastic solid, it is standard to enforce continuity of the normal velocities and of the normal stresses at the interface between the fluid and the solid. In a numerical scheme, there are many ways that velocityand stress-continuity can be enforced in the discrete(More)
Methods for the numerical discretization of the Vlasov equation should efficiently use the phase-space discretization and should introduce only enough numerical dissipation to promote stability and control oscillations. A new high-order nonlinear finite-volume algorithm for the Vlasov equation that discretely conserves particle number and controls(More)
Stable partitioned algorithms for fluid-structure interaction (FSI) problems are developed and analyzed in this two-part paper. Part I describes an algorithm for incompressible flow coupled with compressible elastic solids, while Part II discusses an algorithm for incompressible flow coupled with structural shells. The numerical approach described here for(More)
We develop new high-order accurate upwind schemes for the wave equation in second-order form. These schemes are developed directly for the equations in second-order form, as opposed to transforming the equations to a first-order hyperbolic system. The schemes are based on the solution to a local Riemann-type problem that uses d’Alembert’s exact solution. We(More)
The estimation of discretization error in numerical simulations is a key component in the development of uncertainty quantification. In particular, there exists a need for reliable, robust estimators for finite volume and finite difference discretizations of hyperbolic partial differential equations. The approach espoused here, often called the error(More)
Numerical error estimation for time dependent hyperbolic problems is challenging for theoretical and practical reasons. In these systems, error can propagate long distances and produce effects far from the point of generation. In addition, nonlinear interactions of error, as well as discretization nonlinearities can play important roles and must be(More)