# Daniel T. Graves

Dan Graves
Computer Systems Engineer
Phone: +1 510 486 8697
Fax: +1 510 486 6900

Dr. Daniel Graves received his BS from the University  of New Hampshire in 1989.  He received his Ph.D. from the University of California, Berkeley in 1996.  Both degrees were in Mechanical Engineering.  He has worked at Lawrence Berkeley National Laboratory since 1997.  He is a senior member of the Applied Numerical Algorithms Group.

His research is in the area of numerical methods for partial differential equations, with contributions in the areas of adaptive mesh refinement, Cartesian grid embedded boundary methods, massively parallel computation and library design for scientific computing.  He has contributed significantly in algorithms for incompressible flow, shock physics, viscoelastic flows and elliptic solvers for magneto-hydrodynamics.

## Journal Articles

### Daniel T. Graves, Phillip Colella, David Modiano, Jeffrey Johnson, Bjorn Sjogreen, Xinfeng Gao,"A Cartesian Grid Embedded Boundary Method for the Compressible Navier Stokes Equations",Communications in Applied Mathematics and Computational Science,December 23, 2013,

In this paper, we present an unsplit method for the time-dependent
compressible Navier-Stokes equations in two and three dimensions.
We use a a conservative, second-order Godunov algorithm.
We use a Cartesian grid, embedded boundary method to resolve complex
boundaries.  We solve for viscous and conductive terms with a
second-order semi-implicit algorithm.  We demonstrate second-order
accuracy in solutions of smooth problems in smooth geometries and
demonstrate robust behavior for strongly discontinuous initial
conditions in complex geometries.

## Reports

### Brian Van Straalen, David Trebotich, Terry Ligocki, Daniel T. Graves, Phillip Colella, Michael Barad,"An Adaptive Cartesian Grid Embedded Boundary Method for the Incompressible Navier Stokes Equations in Complex Geometry",LBNL Report Number: LBNL-1003767,2012,LBNL LBNL Report Numb,

We present a second-order accurate projection method to solve the
incompressible Navier-Stokes equations on irregular domains in two
and three dimensions.  We use a finite-volume discretization
obtained from intersecting the irregular domain boundary with a
Cartesian grid.  We address the small-cell stability problem
associated with such methods by hybridizing a conservative
discretization of the advective terms with a stable, nonconservative
discretization at irregular control volumes, and redistributing the
difference to nearby cells.  Our projection is based upon a
finite-volume discretization of Poisson's equation.  We use a
second-order, $L^\infty$-stable algorithm to advance in time.  Block
structured local refinement is applied in space.  The resulting
method is second-order accurate in $L^1$ for smooth problems.  We
demonstrate the method on benchmark problems for flow past a
cylinder in 2D and a sphere in 3D as well as flows in 3D geometries
obtained from image data.