阅读说明：本技术 天然河道一维水动力高精度数值模拟方法 (High-precision numerical simulation method for one-dimensional water power of natural river ) 是由 孙万光 马军 栾宇东 范宝山 杨海滔 唐振华 姜彪 蒋攀 赵浩 于 2021-08-26 设计创作，主要内容包括：本发明提供了天然河道一维水动力高精度数值模拟方法,涉及计算流体动力学技术领域,包括守恒型圣维南方程、采用Godunov格式的有限体积法对控制方程离散、HLLC近似Riemann求解器、变量空间重构、采用二阶龙格—库塔离散的时间分裂方法来处理源项,本发明基于Godunov格式,提出了HLLC近似Riemann求解器的通量计算方法,并拓展至守恒型圣维南方程；提出了针对天然河道复杂断面几何形状下的变量空间重构方法：依据过流断面面积和静力矩等效原则将河道断面概化成矩形,通过线性插值构造单元界面处断面几何形状,根据水位重构结果计算界面两侧过流断面面积和静力矩的重构值,保证计算格式守恒。本发明为天然河道水动力及环境水力学高精度数值模拟提供了新的方法。(The invention provides a high-precision numerical simulation method for one-dimensional hydrodynamic force of a natural river channel, which relates to the technical field of computational fluid dynamics and comprises a conservation type Saint-Venn equation, a finite volume method adopting a Godunov format to discretize a control equation, an HLLC approximate Riemann solver, a variable space reconstruction and a time splitting method adopting second-order Runge-Kutta discretization to process source items, wherein the invention provides a flux calculation method of the HLLC approximate Riemann solver based on the Godunov format and expands the flux calculation method to the conservation type Saint-Venn equation; a variable space reconstruction method aiming at the complex cross section geometry of a natural river channel is provided: the river channel section is generalized into a rectangle according to the equivalent principle of the flow cross-section area and the static moment, the cross-section geometry at the unit interface is constructed through linear interpolation, the reconstruction values of the flow cross-section area and the static moment on the two sides of the interface are calculated according to the water level reconstruction result, and the conservation of the calculation format is ensured. The invention provides a new method for high-precision numerical simulation of natural river hydrodynamic force and environmental hydraulics.)

1. The high-precision numerical simulation method of the one-dimensional hydrodynamic force of the natural river channel is characterized by comprising the following steps of: the method comprises the following steps:

s1, conservation type Saint Vietnam equation;

s2, discretizing a control equation by adopting a finite volume method in a Godunov format;

s3, an HLLC approximation Riemann solver based on a conservation type Saint-Venn equation;

s4, reconstructing a variable space;

s5, the source item is processed by a second-order Runge-Kutta discrete time splitting method.

2. The method for high-precision numerical simulation of one-dimensional hydrodynamic force of a natural river according to claim 1, wherein the method comprises the following steps: a conservation type Saint Vietnam equation set is adopted, and the expression is as follows:

in the formula: u is a variable; f is flux; s is a source item; t is time; x is a spatial coordinate; a (x, t) is the flow cross-section area; q is the flow; g is the acceleration of gravity; s₀Is the bed surface slope; s_fIs the friction drag ratioReducing; i is₁And I₂Static moment and side pressure, respectively, the expression is as follows:

in the formula: h is the depth of water, and b (x, η) is the width of the section.

3. The method for high-precision numerical simulation of one-dimensional hydrodynamic force of a natural river according to claim 1, wherein the method comprises the following steps: the method for calculating the flux of the HLLC approximate Riemann solver based on the conservation type Saint-Venn equation is provided, and the solver is expanded from a shallow water equation to the conservation type Saint-Venn equation:

in the formula: u shape_LAnd U_RVariables on the left and right sides of the interface respectively; f_LAnd F_RLeft and right interfacial flux, respectively; u shape_*LAnd U_*RRespectively a left variable and a right variable of the intermediate wave, which are variables to be solved; f_*LAnd F_*RThe flux on the left side and the right side of the middle wave respectively; s_LAnd S_RThe wave velocities of the left side and the right side of the interface respectively;

for calculating the interface flux, U is also needed_*LAnd U_*RA value of (d); the following assumptions are incorporated here:

A_*L＝A_*R＝A_*,Q_*L＝Q_*R＝Q_*,S_*＝Q_*/A_* (11)

in fact, the above assumptions are also true for the exact Riemann solver. Deducing to obtain a medium wave variable U based on a conservation type Saint-Vietnam equation_*＝[A_*,Q_*]^TAnd the velocity S of the intermediate wave_*Expression (c):

for cross wave velocity S_L、S_RAnd S_*Respectively using Rankine-Hugoniot conditions, available:

taking the first component of equation (2), i.e., the mass conservation equation, into the first two terms of equation (12), and taking equation (11) into it, one can obtain:

the above formula relates to Q_*And A_*The system of equations (a) can be solved to obtain:

。

4. the method for high-precision numerical simulation of one-dimensional hydrodynamic force of a natural river according to claim 1, wherein the method comprises the following steps: a variable space reconstruction method aiming at the complex cross section geometry of a natural river channel is provided: the river channel section is generalized into a rectangle according to the equivalent principle of the flow cross-section area and the static moment, the cross-section geometry at the unit interface is constructed through linear interpolation, the reconstruction values of the flow cross-section area and the static moment on the two sides of the interface are calculated according to the water level reconstruction result, and the conservation of the calculation format is ensured. The method comprises the following specific steps:

a) natural river section generalization method

The river water level is given, and the flow cross section area A and the static moment I are calculated firstly₁According to the equivalent principle of flow cross-section area and static moment, the natural river channel cross-section is generalized to be a rectangle, namely: a '═ A, I'₁＝I₁Wherein A ', I'₁Respectively an equivalent overflowing section area and an equivalent static moment, so that equivalent water depth h ', equivalent river width B' and equivalent river bottom elevation Z 'of the overflowing section can be deduced'_bThe expression is as follows:

the water depth is a key parameter for wave velocity calculation, the natural river usually adopts h as A/B to calculate the average water depth of the section, wherein B is the water surface width, however, for a compound section, B and h have mutation, obvious influence is generated on variable space reconstruction, and the equivalent water depth and the equivalent water width do not have mutation, the generalization method ensures that the stress condition of the unit water body is unchanged, the physical concept is clear, and the generalization result of the equivalent water width and the equivalent water depth is unique;

b) cross-sectional geometry configuration at cell interface

Constructing the section geometry at the unit interface through linear interpolation according to the width and the bottom elevation of the generalized adjacent river channel section; taking the cross-sectional geometry configuration at the i +1/2 interface as an example, the expression is as follows:

c) variable space reconstruction

Variables requiring spatial reconstruction include A, Q and I₁(ii) a Firstly, the MUSCL method is adopted to construct the water level at the interfaceAnd flow rateThen based onAnd constructing the flow cross-sectional area and the static moment at the interface, wherein the expression is as follows:

Technical Field

The invention relates to the technical field of computational fluid dynamics, in particular to a high-precision numerical simulation method for one-dimensional hydrodynamic force of a natural river channel.

Background

The one-dimensional unsteady flow numerical simulation of the natural river is widely applied in the fields of water conservancy planning design, flood control, disaster reduction and the like; the geometrical shape of the cross section of a natural river channel, particularly a mountain river channel, is changed rapidly, the river bottom gradient is changed greatly, and the flow state of water flow can generate the phenomenon of alternation of rapid flow and slow flow; in addition, the phenomena of ice plugs and ice dams of rivers in high-latitude severe cold regions frequently occur, shock wave interruption occurs under the dam after the ice dam is broken, the shock wave interruption belongs to shallow water interrupted flow, strong nonlinearity is realized due to sudden change of hydraulic elements at the interruption positions, and the traditional numerical calculation method (such as finite difference) is prone to failure.

For the intermittent problem, on a control equation, the solution of a conservation numerical value format can be converged to the weak solution of a conservation control equation, the intermittent problem is solved by adopting a non-conservation control equation to obtain an error result, the equations are only effective on smooth flow, and for the intermittent problem, the shock wave velocity calculated according to a jumping condition is wrong; in the numerical calculation method, the Godunov format is popular because of strong discontinuous problem processing capability. Under the Godunov format, the Riemann problem of the homogeneous shallow water equation set is defined as an initial value problem with constant piecewise variables, a flux value at a unit interface can be obtained by adopting an accurate Riemann solver, the precision is high, but the nonlinear algebraic identity needs to be iteratively solved, and the consumption of computing resources is increased. In order to simplify the calculation, various approximate Riemann solvers are rapidly developed, such as a Roe method, an HLL method and the like, and the Roe linearization Riemann solver has the following defects: firstly, in transcritical flow or shock wave simulation, entropy correction is needed to avoid non-matter understanding; secondly, under the action of strong sparse waves (in an area with very shallow water flow), calculating the negative value of the water depth by a linearized Riemann solver; and thirdly, under the interaction of strong waves, the linearized Riemann solution generally lacks robustness. The HLL approximation Riemann solver simplifies the wave family into 2, is only suitable for a one-dimensional system with 2 equations, and has poor simulation precision on contact discontinuity and shear waves. The HLLC solver is a 3-wave family model, and can accurately solve the problems of contact discontinuity and shear wave; compared with an HLL solver, the HLLC solver can expand a concentration component equation, favorable conditions are created for the simulation of the environmental hydraulics of the natural river channel, the popularization and application prospects are very wide, in the past research, the HLLC solver is mostly adopted to solve a shallow water equation, the one-dimensional water power of the natural river channel usually takes an Saint-Venn equation as a control equation, the HLLC solver is adopted to solve the Saint-Venn equation, and reports are rarely seen so far.

In order to obtain a high-precision numerical solution in Godunov format, variable space reconstruction is generally required, and a variable space reconstruction method represented by MUSCL (monomer Upstream-centered Scheme for subsequent law) is widely applied, but the method is only suitable for variable space reconstruction under the condition of gradually changing section, the geometric shape of the section of a natural river channel is complex, the river width and the water depth are rapidly changed along the way, and the direct adoption of the MUSCL method for variable space reconstruction can generate a large error.

Disclosure of Invention

The invention aims to provide a high-precision numerical simulation method for one-dimensional hydrodynamic force of a natural river channel, which adopts a conservation type Saint Vinan equation as a control equation for one-dimensional non-constant flow of the natural river channel, provides a variable space reconstruction method under the condition of rapid change of the geometric shape of the cross section of the natural river channel based on a Godunov format, deduces a flux calculation formula of an HLLC solver based on the conservation type Saint Vinan equation, and provides a high-precision, simple and convenient method for the numerical simulation of the complex hydrodynamic force of the natural river channel.

In order to achieve the purpose, the invention provides the following technical scheme: the high-precision numerical simulation method for the one-dimensional hydrodynamic force of the natural river comprises the following steps:

s1, conservation type Saint Vietnam equation;

s2, discretizing a control equation by adopting a finite volume method in a Godunov format;

s3, an HLLC approximation Riemann solver based on a conservation type Saint-Venn equation;

s4, reconstructing a variable space;

s5, the source item is processed by a second-order Runge-Kutta discrete time splitting method.

Preferably, a conservation type saint-vican equation set is adopted, and the expression is as follows:

in the formula: u is a variable; f is flux; s is a source item; t is time; x is a spatial coordinate; a (x, t) is the flow cross-section area; q is the flow; g is the acceleration of gravity; s₀Is the bed surface slope; s_fIs the friction drag ratio drop; i is₁And I₂Static moment and side pressure, respectively, the expression is as follows:

in the formula: h is the depth of water, and b (x, η) is the width of the section.

Preferably, a flux calculation method of an HLLC approximation Riemann solver based on a conservation type Saint-Venn equation is provided, and the solver is expanded from a shallow water equation to the conservation type Saint-Venn equation:

in the formula: u shape_LAnd U_RVariables on the left and right sides of the interface respectively; f_LAnd F_RLeft and right interfacial flux, respectively; u shape_*LAnd U_*RRespectively a left variable and a right variable of the intermediate wave, which are variables to be solved; f_*LAnd F_*RThe flux on the left side and the right side of the middle wave respectively; s_LAnd S_RThe left and right wave velocities of the interface, respectively.

For calculating the interface flux, U is also needed_*LAnd U_*RA value of (d); the following assumptions are incorporated here:

A_*L＝A_*R＝A_*,Q_*L＝Q_*R＝Q_*,S_*＝Q_*/A_* (11)

in fact, the above assumptions are also true for the exact Riemann solver. Deducing to obtain a medium wave variable U based on a conservation type Saint-Vietnam equation_*＝[A_*,Q_*]^TAnd the velocity S of the intermediate wave_*Expression (c):

for cross wave velocity S_L、S_RAnd S_*The conditions of (1) are respectively applied to Rankine-Hugoniot conditions, and the following can be obtained:

taking the first component of equation (2), i.e., the mass conservation equation, into the first two terms of equation (12), and taking equation (11) into it, one can obtain:

the above formula relates to Q_*And A_*The system of equations (a) can be solved to obtain:

preferably, a variable space reconstruction method aiming at the complex cross section geometry of the natural river is provided: the river channel section is generalized into a rectangle according to the equivalent principle of the flow cross-section area and the static moment, the cross-section geometry at the unit interface is constructed through linear interpolation, the reconstruction values of the flow cross-section area and the static moment on the two sides of the interface are calculated according to the water level reconstruction result, and the conservation of the calculation format is ensured. The method comprises the following specific steps:

a) natural river section generalization method

The river water level is given, and the flow cross section area A and the static moment I are calculated firstly₁According to the equivalent principle of flow cross-section area and static moment, the natural river channel cross-section is generalized to be a rectangle, namely: a '═ A, I'₁＝I₁Wherein A ', I'₁Respectively, an equivalent flow cross-sectional area and an equivalent static moment. Therefore, equivalent water depth h ', equivalent river width B' and equivalent river bottom elevation Z 'of the overflowing section can be deduced'_bThe expression is as follows:

the water depth is a key parameter for wave velocity calculation, the natural river usually adopts h as A/B to calculate the average water depth of the section, wherein B is the water surface width, however, for a compound section, B and h have mutation, obvious influence is generated on variable space reconstruction, and the equivalent water depth and the equivalent water width do not have mutation, the generalization method ensures that the stress condition of the unit water body is unchanged, the physical concept is clear, and the generalization result of the equivalent water width and the equivalent water depth is unique;

b) cross-sectional geometry configuration at cell interface

Constructing the section geometry at the unit interface through linear interpolation according to the width and the bottom elevation of the generalized adjacent river channel section; taking the cross-sectional geometry configuration at the i +1/2 interface as an example, the expression is as follows:

c) variable space reconstruction

Variables requiring spatial reconstruction include A, Q and I₁(ii) a Firstly, the MUSCL method is adopted to construct the water level at the interfaceAnd flow rateThen based onAnd constructing the flow cross-sectional area and the static moment at the interface, wherein the expression is as follows:

compared with the prior art, the invention has the beneficial effects that: the invention provides a flux calculation method of an HLLC approximate Riemann solver based on a conservation type Saint-Venn equation based on a Godunov format, and the solver is expanded to the conservation type Saint-Venn equation from a shallow water equation; a variable space reconstruction method aiming at the complex cross section geometry of a natural river channel is provided: the river channel cross section is generalized into a rectangle according to the equivalent principle of the overflow cross section area and the static moment, the cross section geometry at the interface of the unit is constructed through linear interpolation, the reconstruction values of the overflow cross section area and the static moment at two sides of the interface are calculated according to the water level reconstruction result, and the conservation of the calculation format is ensured.

Of course, it is not necessary for any product in which the invention is practiced to achieve all of the above-described advantages at the same time.

Drawings

In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.

FIG. 1 is a center format finite volume method unit discretization;

FIG. 2 is an HLLC approximate Riemann solver wave structure;

FIG. 3 is a schematic view of a multiple section;

FIG. 4 is a comparison of the average water depth of the profile and the equivalent water depth;

FIG. 5 is a schematic plan view and a cross-sectional layout of a river;

FIG. 6 is a typical measured cross-section and a generalized cross-section of a river;

FIG. 7 is a comparison of the calculated value and the measured value of the maximum water level of the cross section

In the drawings, the components represented by the respective reference numerals are listed below:

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.

Referring to fig. 1-7, the present invention provides a technical solution: the high-precision numerical simulation method for the one-dimensional hydrodynamic force of the natural river comprises the following steps:

s1, conservation type Saint Vietnam equation;

s2, discretizing a control equation by adopting a finite volume method in a Godunov format;

s3, an HLLC approximation Riemann solver based on a conservation type Saint-Venn equation;

s4, reconstructing a variable space;

s5, the source item is processed by a second-order Runge-Kutta discrete time splitting method.

Wherein, a conservation type Saint Vietnam equation set is adopted, and the expression is as follows:

in the formula: u is a variable; f is flux; s is a source item; t is time; x is a spatial coordinate; a (x, t) is the flow cross-section area; q is the flow; g is the acceleration of gravity; s₀Is the bed surface slope; s_fIs the friction drag ratio drop; i is₁And I₂Static moment and side pressure, respectively, the expression is as follows:

in the formula: h is the depth of water, and b (x, η) is the width of the section.

The method comprises the following steps of providing a flux calculation method of an HLLC approximate Riemann solver based on a conservation type Saint-Venn equation, and expanding the solver from a shallow water equation to the conservation type Saint-Venn equation:

in the formula: u shape_LAnd U_RVariables on the left and right sides of the interface respectively; f_LAnd F_RLeft and right interfacial flux, respectively; u shape_*LAnd U_*RRespectively a left variable and a right variable of the intermediate wave, which are variables to be solved; f_*LAnd F_*RThe flux on the left side and the right side of the middle wave respectively; s_LAnd S_RThe wave velocities of the left side and the right side of the interface respectively;

for calculating the interface flux, U is also needed_*LAnd U_*RA value of (d); the following assumptions are incorporated here:

A_*L＝A_*R＝A_*,Q_*L＝Q_*R＝Q_*,S_*＝Q_*/A_* (11)

in fact, the above assumptions are also true for the exact Riemann solver. Deducing to obtain a medium wave variable U based on a conservation type Saint-Vietnam equation_*＝[A_*,Q_*]^TAnd the velocity S of the intermediate wave_*Expression (c):

for cross wave velocity S_L、S_RAnd S_*The conditions of (1) are respectively applied to Rankine-Hugoniot conditions, and the following can be obtained:

taking the first component of equation (2), i.e., the mass conservation equation, into the first two terms of equation (12), and taking equation (11) into it, one can obtain:

the above formula relates to Q_*And A_*The system of equations (a) can be solved to obtain:

the method comprises the following steps of: the river channel section is generalized into a rectangle according to the equivalent principle of the flow cross-section area and the static moment, the cross-section geometry at the unit interface is constructed through linear interpolation, the reconstruction values of the flow cross-section area and the static moment on the two sides of the interface are calculated according to the water level reconstruction result, and the conservation of the calculation format is ensured. The method comprises the following specific steps:

a) natural river section generalization method

The river water level is given, and the flow cross section area A and the static moment I are calculated firstly₁According to the equivalent principle of flow cross-section area and static moment, the natural river channel cross-section is generalized to be a rectangle, namely: a '═ A, I'₁＝I₁Wherein A ', I'₁Respectively an equivalent overflowing section area and an equivalent static moment, so that equivalent water depth h ', equivalent river width B' and equivalent river bottom elevation Z 'of the overflowing section can be deduced'_bThe expression is as follows:

the water depth is a key parameter for wave velocity calculation, the natural river usually adopts h as A/B to calculate the average water depth of the section, wherein B is the water surface width, however, for a compound section, B and h have mutation, obvious influence is generated on variable space reconstruction, and the equivalent water depth and the equivalent water width do not have mutation, the generalization method ensures that the stress condition of the unit water body is unchanged, the physical concept is clear, and the generalization result of the equivalent water width and the equivalent water depth is unique;

b) cross-sectional geometry configuration at cell interface

Constructing the section geometry at the unit interface through linear interpolation according to the width and the bottom elevation of the generalized adjacent river channel section; taking the cross-sectional geometry configuration at the i +1/2 interface as an example, the expression is as follows:

c) variable space reconstruction

Variables requiring spatial reconstruction include A, Q and I₁(ii) a Firstly, the MUSCL method is adopted to construct the water level at the interfaceAnd flow rateThen based onAnd constructing the flow cross-sectional area and the static moment at the interface, wherein the expression is as follows:

one specific application of this embodiment is:

the plane shape of a river channel of a certain river is changed greatly through basins and canyons, the river width under the normal water level is changed within the range of 200-1000 m, the schematic view of the plane of the river channel is shown in figure 5, the length of the river reach is 59.44km, and 18 actually measured large sections (0-17) are arranged.

The typical cross section of the river is shown in figure 6; the basin river section is a compound section, the river width is wide, the gorge section is a V-shaped section, the river width is small, the longitudinal section of the river bed fluctuates severely, the minimum point elevation of the deep body is-48.67 m, and the maximum point elevation of the deep body is 33.3 m. The river reach has flood with frequency P4% and peak flow 44400m in 1994³And/s, accurately measuring flood marks of all sections after the flood passes, wherein the flood surface line data of the field is complete and accurate and can be used as the basis for river course roughness calibration and calculation result verification.

The high-precision numerical simulation method for the one-dimensional hydrodynamic force of the natural river comprises the following steps:

firstly, carrying out linear reconstruction on basic variables of each unit according to equations (19) to (21) to obtain variable values at an interface;

secondly, calculating the wave velocity of the shallow water wave;

thirdly, calculating the interface flux according to the formula (7) and the formula (14);

a, Q for the next time period.

Comparing the highest water level calculated by the section with the actually measured flood mark, wherein the result is shown in figure 7 (the method is called as HLLC for short), for the convenience of comparison, a one-dimensional unsteady flow numerical calculation model is established by adopting the same section data and boundary conditions based on HEC-RAS software, and a typical flood process in 1994 (called as' HEC-RAS for short) is calculated; the HEC-RAS software non-constant flow control equation is non-conservative, the model is solved by adopting finite difference, the non-constant flow control equation in the literature is also non-conservative, and the method is based on Godunov format, adopts HLL approximate Riemann solver to solve, and adopts the method to synchronously compare (called 'HLL' for short).

As can be seen from FIG. 7, the calculation result based on the HLLC algorithm is well matched with the measured value, the simulation results of the HEC-RAS and HLL methods have large deviation from the measured value, the starting point of the deviation is located on the 9# section, the river surface ratio drop of the 9# to 8# section is obviously higher than the measured value, the calculation results of the upstream water level of the 9# section are both higher than the measured value, wherein the deviation of the HEC-RAS method can reach 1.69m (located on the 11# section) to the maximum, and the deviation of the HLL method can reach 1.42m (located on the 10# section) to the maximum.

The geometric shape of the cross section of the natural river channel is changed rapidly, the relation between the water depth and the flow cross section area between the cross sections is large, the 8# cross section and the 9# cross section are taken as examples (see figure 6), and the flow cross section area of the 8# cross section under the highest water level condition is 9595m²The equivalent water depth is 47.13 m; and the flow cross-sectional area of the No. 9 cross section is 17133m²The equivalent water depth is 1.79 times of that of the 8# section, the equivalent water depth is 33.9m, and the equivalent water depth is 0.72 times of that of the 8# section, and if the variable space reconstruction is directly carried out, a large error is generated, the flux calculation result is seriously distorted, and the problem of format non-conservation is also generated. The cross section geometric shape at the interface of the unit is artificially constructed, the water level reconstruction value based on the MUSCL method at the interface is adopted to calculate the corresponding flow cross section area and static moment, and the flow cross section area and the static moment are used as the variable space reconstruction result, so that the influence of the quick change of the cross section geometric shape on the variable space reconstruction is successfully avoided, and the conservation of the calculation format is ensured.

In the description herein, references to the description of "one embodiment," "an example," "a specific example" or the like are intended to mean that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the invention. In this specification, the schematic representations of the terms used above do not necessarily refer to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples.

The preferred embodiments of the invention disclosed above are intended to be illustrative only. The preferred embodiments are not intended to be exhaustive or to limit the invention to the precise embodiments disclosed. Obviously, many modifications and variations are possible in light of the above teaching. The embodiments were chosen and described in order to best explain the principles of the invention and the practical application, to thereby enable others skilled in the art to best utilize the invention. The invention is limited only by the claims and their full scope and equivalents.