Understanding the Boundary Stencil Effects on the Adjacent Field Resolution in Compact Finite Differences

When establishing the spatial resolution character of a composite compact finite differencing template for high-order field solutions, the stencils selected at nonperiodic boundaries are commonly treated independent of the interior scheme. This position quantifies a false influence of the boundary scheme on the resultant interior dispersive and dissipative consequences of the compound template. Of the three ingredients inherent in the composite template, only its numerical accuracy and global stability have been properly treated in a coupled fashion. Herein, we present a companion means for quantifying the resultant spatial resolution properties that lead to improved predictions of the salient problem physics. Compact boundary stencils with free parameters to minimize the field dispersion (or phase error) and dissipation are included in the procedure. Application of the coupled templates for resolving the viscous Burgers wave and two-dimensional acoustic scattering reveal significant differences in the predictive error.

The Effects of the Boundary Stencils on the Field Spatial Resolution When Using Compact Finite Differences

When establishing the spatial resolution character of a composite compact finite differencing template for high-order field solutions, the stencils selected at non-periodic boundaries are commonly treated independent of the interior scheme. This position quantifies a false influence of the boundary scheme on the resultant interior dispersive and dissipative consequences of the compound template. Of the three ingredients inherent in the composite template, only its numerical accuracy and global stability have been properly treated in a coupled fashion. Herein, we present a companion means for quantifying the resultant spatial resolution properties. Compact boundary stencils with free parameters to minimize the field dispersion (or phase error) and dissipation are included in the proposed procedure. Application of the couples templates to Burgers equation at the non-periodic boundary showed significant differences in the predictive error.

Computational Modeling of Ventricular Mechanics and Energetics

The system of equations, material constitutive laws, and boundary conditions required to construct an anatomically and biophysically based model of ventricular mechanics is reviewed. The models use high-order field descriptions to represent the geometry and embedded microstructural information relevant to whole organ function. Constitutive laws are presented which characterize the nonlinear passive elasticity of cardiac tissue and model the active development of tension produced by myocyte contraction. Finally, the integration of metabolic energetics with organ-scale mechanical simulations is discussed and future research directions are proposed.