12 citations · 30 across the 10 of their papers we have counts for
10 papers
Compact implicit high-resolution numerical scheme for multicomponent transport problems with Langmuir sorption
Dagmar Zakova, Peter Frolkovic
We present a compact implicit high-resolution finite volume scheme for one-dimensional multicomponent transport problems with nonlinear Langmuir sorption. The method combines a sec…
Unconditionally local bounds preserving numerical scheme based on inverse Lax-Wendroff procedure for advection on networks
Peter Frolkovič, Svetlana Krišková, Katarína Lacková
We derive an implicit numerical scheme for the solution of advection equation where the roles of space and time variables are exchanged using the inverse Lax-Wendroff procedure. Th…
Eikonal boundary condition for level set method
Jooyoung Hahn, Karol Mikula, Peter Frolkovič
In this paper, we propose to use the eikonal equation as a boundary condition when advective or normal flow equations in the level set formulation are solved numerically on polyhed…
Compact implicit high resolution numerical method for solving transport problems with sorption isotherms
Dagmar Zakova, Peter Frolkovic
This study investigates numerical methods to solve nonlinear transport problems characterized by various sorption isotherms with a focus on the Freundlich type of isotherms. We des…
Numerical solution of two dimensional scalar conservation laws using compact implicit numerical schemes on Cartesian meshes
Peter Frolkovic, Dagmar Zakova
This paper deals with the numerical solution of conservation laws in the two dimensional case using a novel compact implicit time discretization that enables applications of fast a…
Unconditionally stable higher order semi-implicit level set method for advection equations
Peter Frolkovič, Nikola Gajdošová
We present compact semi-implicit finite difference schemes on structured grids for numerical solutions of the advection by an external velocity and by a speed in normal direction t…
Laplacian regularized eikonal equation with Soner boundary condition on polyhedral meshes
Jooyoung Hahn, Karol Mikula, Peter Frolkovič
In this paper, we propose a numerical algorithm based on a cell-centered finite volume method to compute a distance from given objects on a three-dimensional computational domain d…
Semi-implicit methods for advection equations with explicit forms of numerical solution
Peter Frolkovič, Svetlana Krišková, Michaela Rohová +1
We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions c…
Semi-implicit second order schemes for numerical solution of level set advection equation on Cartesian grids
Peter Frolkovič, Karol Mikula
A new parametric class of semi-implicit numerical schemes for a level set advection equation on Cartesian grids is derived and analyzed. An accuracy and a stability study is provid…
Higher order semi-implicit schemes for linear advection equation on Cartesian grids with numerical stability analysis
Peter Frolkovič, Karol Mikula
A new class of semi-implicit numerical schemes for linear advection equation on Cartesian grids is derived that is inspired by so-called -schemes used with fully explicit discre…