Pressure Decimation and Interpolation (PDI) method for a baroclinic non-hydrostatic model

Abstract

Non-hydrostatic models are computationally expensive in simulating density flows and mass transport problems due to the requirement of sufficient grid resolution to resolve density and flow structures. Numerical tests based on the Non-Hydrostatic Wave Model, NHWAVE [Ma et al., 2012], indicated that up to 70% of the total computational cost may be born by the pressure Poisson solver in cases with high grid resolution in both vertical and horizontal directions. However, recent studies using Poisson solver-based non-hydrostatic models have shown that an accurate prediction of wave dispersion does not require a large number of vertical layers if the dynamic pressure is properly discretized. In this study, we explore the possibility that the solution for the dynamic pressure field may, in general, be decimated to

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

“…This observation, and inspired by the work of Van Reeuwijk (2002) and Shi et al (2015), motivates us to solve the vertical and horizontal momentum balances on essentially separate grids. The vertical balance (and pressure) is evaluated on a coarse grid of which the resolution is dictated by the wave motion, whereas the horizontal balance is solved on a finer grid to account for vertical shear.…”

“…Following Shi et al (2015) we describe the pressure by a spline curveq(z) that in each coarse pressure layer takes the form of a polynomial of order…”

“…To uniquely specify the coefficients in terms of the discrete pressures (i.e., α p,n = P m=0 β p,n,m q m ), we need P (N p + 1) restrictions. These follow from enforcing that the first N p − 1 derivatives are continuous at the coarse-grid layer-interfaces, coupled with (for P > 1) the conditions at the surface and bottom (Shi et al, 2015),…”

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

“…This observation, and inspired by the work of Van Reeuwijk (2002) and Shi et al (2015), motivates us to solve the vertical and horizontal momentum balances on essentially separate grids. The vertical balance (and pressure) is evaluated on a coarse grid of which the resolution is dictated by the wave motion, whereas the horizontal balance is solved on a finer grid to account for vertical shear.…”

“…Following Shi et al (2015) we describe the pressure by a spline curveq(z) that in each coarse pressure layer takes the form of a polynomial of order…”

“…To uniquely specify the coefficients in terms of the discrete pressures (i.e., α p,n = P m=0 β p,n,m q m ), we need P (N p + 1) restrictions. These follow from enforcing that the first N p − 1 derivatives are continuous at the coarse-grid layer-interfaces, coupled with (for P > 1) the conditions at the surface and bottom (Shi et al, 2015),…”

Observations and Modeling of a Buoyant Plume Exiting Into a Tidal Cross‐Flow and Exhibiting Along‐Front Instabilities

“…During the observations, the ebb plume front was attached to the western jetty as seen in Figure 1b, extends south, and curves to the southeast. For comparison to the field data, we utilize the NHWAVE non-hydrostatic model (Ma et al, 2013;J. Shi et al, 2015).…”

“…(2013, 2012). Efforts have been made to further improve its computational efficiency (J. Shi et al., 2015) and accuracy (Derakhti et al., 2016) and to produce increasingly realistic simulations of internal waves (J. Shi et al., 2019), and non‐hydrostatic frontal processes in river plumes (F. Shi et al., 2017; Zhou et al., 2017). F. Shi et al.…”

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

“…This observation, and inspired by the work of Van Reeuwijk (2002) and Shi et al (2015), motivates us to solve the vertical and horizontal momentum balances on essentially separate grids. The vertical balance (and pressure) is evaluated on a coarse grid of which the resolution is dictated by the wave motion, whereas the horizontal balance is solved on a finer grid to account for vertical shear.…”

“…Following Shi et al (2015) we describe the pressure by a spline curveq(z) that in each coarse pressure layer takes the form of a polynomial of order…”

“…To uniquely specify the coefficients in terms of the discrete pressures (i.e., α p,n = P m=0 β p,n,m q m ), we need P (N p + 1) restrictions. These follow from enforcing that the first N p − 1 derivatives are continuous at the coarse-grid layer-interfaces, coupled with (for P > 1) the conditions at the surface and bottom (Shi et al, 2015),…”

Observations and Modeling of a Buoyant Plume Exiting Into a Tidal Cross‐Flow and Exhibiting Along‐Front Instabilities

“…During the observations, the ebb plume front was attached to the western jetty as seen in Figure 1b, extends south, and curves to the southeast. For comparison to the field data, we utilize the NHWAVE non-hydrostatic model (Ma et al, 2013;J. Shi et al, 2015).…”

“…(2013, 2012). Efforts have been made to further improve its computational efficiency (J. Shi et al., 2015) and accuracy (Derakhti et al., 2016) and to produce increasingly realistic simulations of internal waves (J. Shi et al., 2019), and non‐hydrostatic frontal processes in river plumes (F. Shi et al., 2017; Zhou et al., 2017). F. Shi et al.…”

Efficient non-hydrostatic modelling of 3D wave-induced currents using a subgrid approach

“…This observation, and inspired by the work of Van Reeuwijk (2002) and Shi et al (2015), motivates us to solve the vertical and horizontal momentum balances on essentially separate grids. The vertical balance (and pressure) is evaluated on a coarse grid of which the resolution is dictated by the wave motion, whereas the horizontal balance is solved on a finer grid to account for vertical shear.…”

“…Following Shi et al (2015) we describe the pressure by a spline curveq(z) that in each coarse pressure layer takes the form of a polynomial of order…”

“…To uniquely specify the coefficients in terms of the discrete pressures (i.e., α p,n = P m=0 β p,n,m q m ), we need P (N p + 1) restrictions. These follow from enforcing that the first N p − 1 derivatives are continuous at the coarse-grid layer-interfaces, coupled with (for P > 1) the conditions at the surface and bottom (Shi et al, 2015),…”

Observations and Modeling of a Buoyant Plume Exiting Into a Tidal Cross‐Flow and Exhibiting Along‐Front Instabilities

“…During the observations, the ebb plume front was attached to the western jetty as seen in Figure 1b, extends south, and curves to the southeast. For comparison to the field data, we utilize the NHWAVE non-hydrostatic model (Ma et al, 2013;J. Shi et al, 2015).…”

“…(2013, 2012). Efforts have been made to further improve its computational efficiency (J. Shi et al., 2015) and accuracy (Derakhti et al., 2016) and to produce increasingly realistic simulations of internal waves (J. Shi et al., 2019), and non‐hydrostatic frontal processes in river plumes (F. Shi et al., 2017; Zhou et al., 2017). F. Shi et al.…”